The goal of this paper is to investigate the theory of Noether solvability for Volterra singular integral equations(VSIEs)with convolution and Cauchy kernels in a more general function class.To obtain the analytic sol...The goal of this paper is to investigate the theory of Noether solvability for Volterra singular integral equations(VSIEs)with convolution and Cauchy kernels in a more general function class.To obtain the analytic solutions,we transform such equations into boundary value problems with discontinuous coefficients by the properties of Fourier analysis.In view of the analytical Riemann-Hilbert method,the generalized Liouville theorem and Sokhotski-Plemelj formula,we get the uniqueness and existence of solutions for such problems,and study the asymptotic property of solutions at nodes.Therefore,this paper improves the theory of singular integral equations and boundary value problems.展开更多
In this study,we explore some of the best proximity point results for generalized proximal contractions in the setting of double-controlled metric-type spaces.A non-trivial example is given to elucidate our analysis,a...In this study,we explore some of the best proximity point results for generalized proximal contractions in the setting of double-controlled metric-type spaces.A non-trivial example is given to elucidate our analysis,and some novel results are derived.The discovered results generalize previously known results in the context of a double controlled metric type space environment.This article’s proximity point results are the first of their kind in the realm of controlled metric spaces.To build on the results achieved in this article,we present an application demonstrating the usability of the given results.展开更多
The main purpose of this paper is to use the Chelyshkov-collocation spectral method for solving nonlinear Quadratic integral equations of Volterra type.The method is based on the approximate solutions in terms of Chel...The main purpose of this paper is to use the Chelyshkov-collocation spectral method for solving nonlinear Quadratic integral equations of Volterra type.The method is based on the approximate solutions in terms of Chelyshkov polynomials with unknown coefficients.The Chelyshkov polynomials and their properties are employed to derive the operational matrices of integral and product.The application of these operational matrices for solving the mentioned problem is explained.The error analysis of the proposed method is investigated.Finally,some numerical examples are provided to demonstrate the efficiency of the method.展开更多
It is well-known that interpolation by rational functions results in a more accurate approximation than the polynomials interpolation.However,classical rational interpolation has some deficiencies such as uncontrollab...It is well-known that interpolation by rational functions results in a more accurate approximation than the polynomials interpolation.However,classical rational interpolation has some deficiencies such as uncontrollable poles and low convergence order.In contrast with the classical rational interpolants,the generalized barycentric rational interpolants which depend linearly on the interpolated values,yield infinite smooth approximation with no poles in real numbers.In this paper,a numerical collocation approach,based on the generalized barycentric rational interpolation and Gaussian quadrature formula,was introduced to approximate the solution of Volterra-Fredholm integral equations.Three types of points in the solution domain are used as interpolation nodes.The obtained numerical results confirm that the barycentric rational interpolants are efficient tools for solving Volterra-Fredholm integral equations.Moreover,integral equations with Runge’s function as an exact solution,no oscillation occurrs in the obtained approximate solutions so that the Runge’s phenomenon is avoided.展开更多
In this paper we will see that, under certain conditions, the techniques of generalized moment problem will apply to numerically solve an Volterra integral equation of first kind or second kind. Volterra integral equa...In this paper we will see that, under certain conditions, the techniques of generalized moment problem will apply to numerically solve an Volterra integral equation of first kind or second kind. Volterra integral equation is transformed into a one-dimensional generalized moment problem, and shall apply the moment problem techniques to find a numerical approximation of the solution. Specifically you will see that solving the Volterra integral equation of first kind f（t） = {a^t K（t, s）x（s）ds a ≤ t ≤ b or solve the Volterra integral equation of the second kind x（t） =f（t）＋{a^t K（t,s）x（s）ds a ≤ t ≤ b is equivalent to solving a generalized moment problem of the form un = {a^b gn（s）x（s）ds n = 0,1,2… This shall apply for to find the solution of an integrodifferential equation of the form x＇（t） = f（t） ＋ {a^t K（t,s）x（s）ds for a ≤ t ≤ b and x（a） = a0 Also considering the nonlinear integral equation： f（x）= {fa^x y（x-t）y（t）dt This integral equation is transformed a two-dimensional generalized moment problem. In all cases, we will find an approximated solution and bounds for the error of the estimated solution using the techniques ofgeneralized moment problem.展开更多
In this article, an extended Taylor expansion method is proposed to estimate the solution of linear singular Volterra integral equations systems. The method is based on combining the m-th order Taylor polynomial of un...In this article, an extended Taylor expansion method is proposed to estimate the solution of linear singular Volterra integral equations systems. The method is based on combining the m-th order Taylor polynomial of unknown functions at an arbitrary point and integration method, such that the given system of singular integral equations is converted into a system of linear equations with respect to unknown functions and their derivatives. The required solutions are obtained by solving the resulting linear system. The proposed method gives a very satisfactory solution,which can be performed by any symbolic mathematical packages such as Maple, Mathematica, etc. Our proposed approach provides a significant advantage that the m-th order approximate solutions are equal to exact solutions if the exact solutions are polynomial functions of degree less than or equal to m. We present an error analysis for the proposed method to emphasize its reliability. Six numerical examples are provided to show the accuracy and the efficiency of the suggested scheme for which the exact solutions are known in advance.展开更多
Integral equations theoretical parts and applications have been studied and investigated in previous works. In this work, results on investigations of the uniqueness of the Fredholm-Stiltjes linear integral equations ...Integral equations theoretical parts and applications have been studied and investigated in previous works. In this work, results on investigations of the uniqueness of the Fredholm-Stiltjes linear integral equations solutions of the third kind were considered. Volterra integral equations of the first and third kind with smooth kernels were studied, and proof of the existence of a multiparameter family of solutions is described. Additionally, linear Fredholm integral equations of the first kind were investigated, for which Lavrent’ev regularizing operators were constructed.展开更多
By means of Fourier integral transformation of generalized function, the fundamental solution for the bending problem of plates on two-parameter foundation is derived in this paper, and the fundamental solution is exp...By means of Fourier integral transformation of generalized function, the fundamental solution for the bending problem of plates on two-parameter foundation is derived in this paper, and the fundamental solution is expanded into a uniformly convergent series. On the basis of the above work, two boundary integral equations which are suitable to arbitrary shapes and arbitrary boundary conditions are established by means of the Rayleigh-Green identity. The content of the paper provides the powerful theories for the application of BEM in this problem.展开更多
This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic So...This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic Sobolev classes, and also gives an optimal algorithm.展开更多
While the approximate solutions of one-dimensional nonlinear Volterra-Fredholm integral equations with smooth kermels are now well understood,no systematic studies of the numerical solutions of their multi-dimensional...While the approximate solutions of one-dimensional nonlinear Volterra-Fredholm integral equations with smooth kermels are now well understood,no systematic studies of the numerical solutions of their multi-dimensional counterparts exist.In this paper,we provide an efficient numerical approach for the multi-dimensional nonlinear Volterra-Fredholm integral equations based on the multi-variate Legendre-collocation approach.Spectral collocation methods for multi-dimensional nonlinear integral equations are known to cause major difficulties from a convergence analysis point of view.Consequently,rigorous error estimates are provided in the weighted Sobolev space showing the exponential decay of the numerical errors.The existence and uniqueness of the numerical solution are established.Numerical experiments are provided to support the theoretical convergence analysis.The results indicate that our spectral collocation method is more flexible with better accuracy than the existing ones.展开更多
Two efficient recursive algorithms epsilon_algorithm and eta_algorithm are introduced to compute the generalized inverse function_valued Padé approximants. The approximants were used to accelerate the convergenc...Two efficient recursive algorithms epsilon_algorithm and eta_algorithm are introduced to compute the generalized inverse function_valued Padé approximants. The approximants were used to accelerate the convergence of the power series with function_valued coefficients and to estimate characteristic value of the integral equations. Famous Wynn identities of the Pad approximants is also established by means of the connection of two algorithms.展开更多
In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equation...In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.展开更多
The universal practices have been centralizing on the research of regularization to the direct boundary integal equations （DBIEs）. The character is elimination of singularities by using the simple solutions. However...The universal practices have been centralizing on the research of regularization to the direct boundary integal equations （DBIEs）. The character is elimination of singularities by using the simple solutions. However, up to now the research of regularization to the first kind integral equations for plane potential problems has never been found in previous literatures. The presentation is mainly devoted to the research on the regularization of the singular boundary integral equations with indirect unknowns. A novel view and idea is presented herein, in which the regularized boundary integral equations with indirect unknowns without including the Cauchy principal value （CPV） and Hadamard-finite-part （HFP） integrals are established for the plane potential problems. With some numerical results, it is shown that the better accuracy and higher efficiency, especially on the boundary, can be achieved by the present system.展开更多
Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic...Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.展开更多
Daubechies interval cally weakly singular Fredholm kind. Utilizing the orthogonality equation is reduced into a linear wavelet is used to solve nurneriintegral equations of the second of the wavelet basis, the integra...Daubechies interval cally weakly singular Fredholm kind. Utilizing the orthogonality equation is reduced into a linear wavelet is used to solve nurneriintegral equations of the second of the wavelet basis, the integral system of equations. The vanishing moments of the wavelet make the wavelet coefficient matrices sparse, while the continuity of the derivative functions of basis overcomes naturally the singular problem of the integral solution. The uniform convergence of the approximate solution by the wavelet method is proved and the error bound is given. Finally, numerical example is presented to show the application of the wavelet method.展开更多
Equivalent Boundary Integral Equations (EBIE) with indirect unknowns for thin elastic plate bending theory, which is equivalent to the original boundary value problem, is established rigorously by mathematical techniq...Equivalent Boundary Integral Equations (EBIE) with indirect unknowns for thin elastic plate bending theory, which is equivalent to the original boundary value problem, is established rigorously by mathematical technique of non-analytic continuation and is fully proved by means of the variational principle. The previous three kinds of boundary integral equations with indirect unknowns are discussed thoroughly and it is shown that all previous results are not EBIE.展开更多
This paper investigates the numerical solution of two-dimensional nonlinear stochastic Itô-Volterra integral equations based on block pulse functions. The nonlinear stochastic integral equation is transformed...This paper investigates the numerical solution of two-dimensional nonlinear stochastic Itô-Volterra integral equations based on block pulse functions. The nonlinear stochastic integral equation is transformed into a set of algebraic equations by operational matrix of block pulse functions. Then, we give error analysis and prove that the rate of convergence of this method is efficient. Lastly, a numerical example is given to confirm the method.展开更多
This paper studies several problems , which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterization...This paper studies several problems , which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterizations of functions in Besom spaces B(?)(0,1) with 0<σ<∞ and (1+σ)-1<γ<∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.展开更多
In recent papers, Babolian & Delves [2] and Belward[3] described a Chebyshev series method for the solution of first kind integral equations. The expansion coefficients of the solution are determined as the soluti...In recent papers, Babolian & Delves [2] and Belward[3] described a Chebyshev series method for the solution of first kind integral equations. The expansion coefficients of the solution are determined as the solution of a mathematical programming problem.The method involves two regularization parameters, Cf and r, but values assigned to these parameters are heuristic in nature. Essah & Delves[7] described an algorithm for setting these parameters automatically, but it has some difficulties. In this paper we describe three iterative algorithms for computing these parameters for singular and non-singular first kind integral equations. We give also error estimates which are cheap to compute. Finally, we give a number of numerical examples showing that these algorithms work well in practice.展开更多
Hypersingular integral equations are derived for the problem of determining the antiplane shear stress around periodic arrays of planar cracks in a periodically-layered anisotropic elastic space. The unknown functions...Hypersingular integral equations are derived for the problem of determining the antiplane shear stress around periodic arrays of planar cracks in a periodically-layered anisotropic elastic space. The unknown functions are directly related to the jump in the displacements across opposite crack faces. Once the integral equations are solved, crack parameters of interest, such as the clack tip stress intensity factors, may be readily computed.For some specific examples of the problem, the integral equations are solved numerically by using a collocation technique, in order to compute the relevant stress intensity factors.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11971015).
文摘The goal of this paper is to investigate the theory of Noether solvability for Volterra singular integral equations(VSIEs)with convolution and Cauchy kernels in a more general function class.To obtain the analytic solutions,we transform such equations into boundary value problems with discontinuous coefficients by the properties of Fourier analysis.In view of the analytical Riemann-Hilbert method,the generalized Liouville theorem and Sokhotski-Plemelj formula,we get the uniqueness and existence of solutions for such problems,and study the asymptotic property of solutions at nodes.Therefore,this paper improves the theory of singular integral equations and boundary value problems.
文摘In this study,we explore some of the best proximity point results for generalized proximal contractions in the setting of double-controlled metric-type spaces.A non-trivial example is given to elucidate our analysis,and some novel results are derived.The discovered results generalize previously known results in the context of a double controlled metric type space environment.This article’s proximity point results are the first of their kind in the realm of controlled metric spaces.To build on the results achieved in this article,we present an application demonstrating the usability of the given results.
文摘The main purpose of this paper is to use the Chelyshkov-collocation spectral method for solving nonlinear Quadratic integral equations of Volterra type.The method is based on the approximate solutions in terms of Chelyshkov polynomials with unknown coefficients.The Chelyshkov polynomials and their properties are employed to derive the operational matrices of integral and product.The application of these operational matrices for solving the mentioned problem is explained.The error analysis of the proposed method is investigated.Finally,some numerical examples are provided to demonstrate the efficiency of the method.
文摘It is well-known that interpolation by rational functions results in a more accurate approximation than the polynomials interpolation.However,classical rational interpolation has some deficiencies such as uncontrollable poles and low convergence order.In contrast with the classical rational interpolants,the generalized barycentric rational interpolants which depend linearly on the interpolated values,yield infinite smooth approximation with no poles in real numbers.In this paper,a numerical collocation approach,based on the generalized barycentric rational interpolation and Gaussian quadrature formula,was introduced to approximate the solution of Volterra-Fredholm integral equations.Three types of points in the solution domain are used as interpolation nodes.The obtained numerical results confirm that the barycentric rational interpolants are efficient tools for solving Volterra-Fredholm integral equations.Moreover,integral equations with Runge’s function as an exact solution,no oscillation occurrs in the obtained approximate solutions so that the Runge’s phenomenon is avoided.
文摘In this paper we will see that, under certain conditions, the techniques of generalized moment problem will apply to numerically solve an Volterra integral equation of first kind or second kind. Volterra integral equation is transformed into a one-dimensional generalized moment problem, and shall apply the moment problem techniques to find a numerical approximation of the solution. Specifically you will see that solving the Volterra integral equation of first kind f（t） = {a^t K（t, s）x（s）ds a ≤ t ≤ b or solve the Volterra integral equation of the second kind x（t） =f（t）＋{a^t K（t,s）x（s）ds a ≤ t ≤ b is equivalent to solving a generalized moment problem of the form un = {a^b gn（s）x（s）ds n = 0,1,2… This shall apply for to find the solution of an integrodifferential equation of the form x＇（t） = f（t） ＋ {a^t K（t,s）x（s）ds for a ≤ t ≤ b and x（a） = a0 Also considering the nonlinear integral equation： f（x）= {fa^x y（x-t）y（t）dt This integral equation is transformed a two-dimensional generalized moment problem. In all cases, we will find an approximated solution and bounds for the error of the estimated solution using the techniques ofgeneralized moment problem.
文摘In this article, an extended Taylor expansion method is proposed to estimate the solution of linear singular Volterra integral equations systems. The method is based on combining the m-th order Taylor polynomial of unknown functions at an arbitrary point and integration method, such that the given system of singular integral equations is converted into a system of linear equations with respect to unknown functions and their derivatives. The required solutions are obtained by solving the resulting linear system. The proposed method gives a very satisfactory solution,which can be performed by any symbolic mathematical packages such as Maple, Mathematica, etc. Our proposed approach provides a significant advantage that the m-th order approximate solutions are equal to exact solutions if the exact solutions are polynomial functions of degree less than or equal to m. We present an error analysis for the proposed method to emphasize its reliability. Six numerical examples are provided to show the accuracy and the efficiency of the suggested scheme for which the exact solutions are known in advance.
文摘Integral equations theoretical parts and applications have been studied and investigated in previous works. In this work, results on investigations of the uniqueness of the Fredholm-Stiltjes linear integral equations solutions of the third kind were considered. Volterra integral equations of the first and third kind with smooth kernels were studied, and proof of the existence of a multiparameter family of solutions is described. Additionally, linear Fredholm integral equations of the first kind were investigated, for which Lavrent’ev regularizing operators were constructed.
文摘By means of Fourier integral transformation of generalized function, the fundamental solution for the bending problem of plates on two-parameter foundation is derived in this paper, and the fundamental solution is expanded into a uniformly convergent series. On the basis of the above work, two boundary integral equations which are suitable to arbitrary shapes and arbitrary boundary conditions are established by means of the Rayleigh-Green identity. The content of the paper provides the powerful theories for the application of BEM in this problem.
基金Project supported by the Natural Science Foundation of China(10371009)Research Fund for the Doctoral Program Higher Education
文摘This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic Sobolev classes, and also gives an optimal algorithm.
文摘While the approximate solutions of one-dimensional nonlinear Volterra-Fredholm integral equations with smooth kermels are now well understood,no systematic studies of the numerical solutions of their multi-dimensional counterparts exist.In this paper,we provide an efficient numerical approach for the multi-dimensional nonlinear Volterra-Fredholm integral equations based on the multi-variate Legendre-collocation approach.Spectral collocation methods for multi-dimensional nonlinear integral equations are known to cause major difficulties from a convergence analysis point of view.Consequently,rigorous error estimates are provided in the weighted Sobolev space showing the exponential decay of the numerical errors.The existence and uniqueness of the numerical solution are established.Numerical experiments are provided to support the theoretical convergence analysis.The results indicate that our spectral collocation method is more flexible with better accuracy than the existing ones.
文摘Two efficient recursive algorithms epsilon_algorithm and eta_algorithm are introduced to compute the generalized inverse function_valued Padé approximants. The approximants were used to accelerate the convergence of the power series with function_valued coefficients and to estimate characteristic value of the integral equations. Famous Wynn identities of the Pad approximants is also established by means of the connection of two algorithms.
基金Project was supported by RFDP of Higher Education and NNSF of China, SF of Wuhan University
文摘In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.
基金Project supported by the National Natural Science Foundation of China (No.10571110)the Natural Science Foundation of Shandong Province of China (No.2003ZX12)
文摘The universal practices have been centralizing on the research of regularization to the direct boundary integal equations （DBIEs）. The character is elimination of singularities by using the simple solutions. However, up to now the research of regularization to the first kind integral equations for plane potential problems has never been found in previous literatures. The presentation is mainly devoted to the research on the regularization of the singular boundary integral equations with indirect unknowns. A novel view and idea is presented herein, in which the regularized boundary integral equations with indirect unknowns without including the Cauchy principal value （CPV） and Hadamard-finite-part （HFP） integrals are established for the plane potential problems. With some numerical results, it is shown that the better accuracy and higher efficiency, especially on the boundary, can be achieved by the present system.
基金This project is supported by National Natural Science Foundation of China(No.50175031).
文摘Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.
基金Supported by the National Natural Science Foundation of China (60572048)the Natural Science Foundation of Guangdong Province(054006621)
文摘Daubechies interval cally weakly singular Fredholm kind. Utilizing the orthogonality equation is reduced into a linear wavelet is used to solve nurneriintegral equations of the second of the wavelet basis, the integral system of equations. The vanishing moments of the wavelet make the wavelet coefficient matrices sparse, while the continuity of the derivative functions of basis overcomes naturally the singular problem of the integral solution. The uniform convergence of the approximate solution by the wavelet method is proved and the error bound is given. Finally, numerical example is presented to show the application of the wavelet method.
文摘Equivalent Boundary Integral Equations (EBIE) with indirect unknowns for thin elastic plate bending theory, which is equivalent to the original boundary value problem, is established rigorously by mathematical technique of non-analytic continuation and is fully proved by means of the variational principle. The previous three kinds of boundary integral equations with indirect unknowns are discussed thoroughly and it is shown that all previous results are not EBIE.
基金NSF Grants 11471105 of China, NSF Grants 2016CFB526 of Hubei Province, Innovation Team of the Educational Department of Hubei Province T201412, and Innovation Items of Hubei Normal University 2018032 and 2018105
文摘This paper investigates the numerical solution of two-dimensional nonlinear stochastic Itô-Volterra integral equations based on block pulse functions. The nonlinear stochastic integral equation is transformed into a set of algebraic equations by operational matrix of block pulse functions. Then, we give error analysis and prove that the rate of convergence of this method is efficient. Lastly, a numerical example is given to confirm the method.
基金The work of the author has been supported by the Deutache Forschungsgemeinschaft(DFG) under Grant Ho 1846/1-1
文摘This paper studies several problems , which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterizations of functions in Besom spaces B(?)(0,1) with 0<σ<∞ and (1+σ)-1<γ<∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.
文摘In recent papers, Babolian & Delves [2] and Belward[3] described a Chebyshev series method for the solution of first kind integral equations. The expansion coefficients of the solution are determined as the solution of a mathematical programming problem.The method involves two regularization parameters, Cf and r, but values assigned to these parameters are heuristic in nature. Essah & Delves[7] described an algorithm for setting these parameters automatically, but it has some difficulties. In this paper we describe three iterative algorithms for computing these parameters for singular and non-singular first kind integral equations. We give also error estimates which are cheap to compute. Finally, we give a number of numerical examples showing that these algorithms work well in practice.
文摘Hypersingular integral equations are derived for the problem of determining the antiplane shear stress around periodic arrays of planar cracks in a periodically-layered anisotropic elastic space. The unknown functions are directly related to the jump in the displacements across opposite crack faces. Once the integral equations are solved, crack parameters of interest, such as the clack tip stress intensity factors, may be readily computed.For some specific examples of the problem, the integral equations are solved numerically by using a collocation technique, in order to compute the relevant stress intensity factors.
