We consider linear partial differential equations of first order on a region . We will see that we can write the equation in partial derivatives as an Fredholm integral equation of the first kind and will solve this l...We consider linear partial differential equations of first order on a region . We will see that we can write the equation in partial derivatives as an Fredholm integral equation of the first kind and will solve this latter with the techniques of inverse problem moments. We will find an approximated solution and bounds for the error of the estimated solution using the techniques on problem of moments.展开更多
We present the numerical method for solution of some linear and non-linear parabolic equation. Using idea [1], we will present the explicit unconditional stable scheme which has no restriction on the step size ratio k...We present the numerical method for solution of some linear and non-linear parabolic equation. Using idea [1], we will present the explicit unconditional stable scheme which has no restriction on the step size ratio k/h2 where k and h are step sizes for space and time respectively. We will also present numerical results to justify the present scheme.展开更多
Asymptotic large- and short-time behavior of solutions of the linear dispersion equation μt = Uxxx in IR× IR＋, and its （2k＋l）th-order extensions are studied. Such a refined scattering is based on a ＂Hermit...Asymptotic large- and short-time behavior of solutions of the linear dispersion equation μt = Uxxx in IR× IR＋, and its （2k＋l）th-order extensions are studied. Such a refined scattering is based on a ＂Hermitian＂ spectral theory for a pair {B,B＊} of non self-adjoint rescaled operators展开更多
The aim of this paper is the introduction of a new approach to 3D modelling of elastic piecewise homogeneous media, in particular Earth crust and upper Mantle. The method is based on the principle of tomography with E...The aim of this paper is the introduction of a new approach to 3D modelling of elastic piecewise homogeneous media, in particular Earth crust and upper Mantle. The method is based on the principle of tomography with Earthquake as a source of the signal and receiver stations on the surface. The wave propagation in solid media is described by a system of three strongly coupled hyperbolic equations with piece - wise constant coefitients. The characteristic set and hi-characteristic curves of this system are computed in a homogeneous half-space with free boundary and the formulae of reflection and diffraction of the hi-characteristics on the internal boundaries of the media. Applications of the characteristic set and bi-eharacteristic curves for the inverse problem in geophysics and Earth modelling are given.展开更多
Aims and Scope The Journal of Computational Mathematics is published bi-monthly.It is an international journal covering all branches of modern computational mathematics such as numerical linear algebra,numerical optim...Aims and Scope The Journal of Computational Mathematics is published bi-monthly.It is an international journal covering all branches of modern computational mathematics such as numerical linear algebra,numerical optimization,computational geometry,numerical PDEs and inverse problems.Papers containing new ideas,creative approaches and/or innovative applications as well as invited reviews are expected to appear regularly in the journal.展开更多
where U and F are the vector-valued functions which are defined on R<sup>+</sup>×R<sup>N</sup> and R<sup>+</sup>×R<sup>N</sup>×R<sup>N</sup>,r...where U and F are the vector-valued functions which are defined on R<sup>+</sup>×R<sup>N</sup> and R<sup>+</sup>×R<sup>N</sup>×R<sup>N</sup>,respectively, U=（u<sub>1</sub>,…,u<sub>N</sub>）, F=（f<sub>1</sub>,…,f<sub>N</sub>）, =（<sub>x</sub><sub>1</sub>,……,<sub>x</sub>）<sub>N</sub>. Moreover, F is smooth enough, andits derivatives of all orders are boundary on R×K. K is any compact set in R<sup>2N</sup>.Obviously,展开更多
In this paper, by exploiting the special block and sparse structure of the coefficient matrix, we present a new preconditioning strategy for solving large sparse linear systems arising in the time-dependent distribute...In this paper, by exploiting the special block and sparse structure of the coefficient matrix, we present a new preconditioning strategy for solving large sparse linear systems arising in the time-dependent distributed control problem involving the heat equation with two different functions. First a natural order-reduction is performed, and then the reduced- order linear system of equations is solved by the preconditioned MINRES algorithm with a new preconditioning techniques. The spectral properties of the preconditioned matrix are analyzed. Numerical results demonstrate that the preconditioning strategy for solving the large sparse systems discretized from the time-dependent problems is more effective for a wide range of mesh sizes and the value of the regularization parameter.展开更多
文摘We consider linear partial differential equations of first order on a region . We will see that we can write the equation in partial derivatives as an Fredholm integral equation of the first kind and will solve this latter with the techniques of inverse problem moments. We will find an approximated solution and bounds for the error of the estimated solution using the techniques on problem of moments.
文摘We present the numerical method for solution of some linear and non-linear parabolic equation. Using idea [1], we will present the explicit unconditional stable scheme which has no restriction on the step size ratio k/h2 where k and h are step sizes for space and time respectively. We will also present numerical results to justify the present scheme.
基金Supported by Shandong Provincial Natural Science Foundation,China(ZR2012AM017)and(2011ZRA07006)partially supported by Jiangsu Planned Projects for Postdoctoral Research Funds(1302022C)+1 种基金China Postdoctoral Science Foundation funded project(2014M551583)Project supported by the National Natural Science Foundation of China(Grant NO.11401302)
文摘Asymptotic large- and short-time behavior of solutions of the linear dispersion equation μt = Uxxx in IR× IR＋, and its （2k＋l）th-order extensions are studied. Such a refined scattering is based on a ＂Hermitian＂ spectral theory for a pair {B,B＊} of non self-adjoint rescaled operators
文摘The aim of this paper is the introduction of a new approach to 3D modelling of elastic piecewise homogeneous media, in particular Earth crust and upper Mantle. The method is based on the principle of tomography with Earthquake as a source of the signal and receiver stations on the surface. The wave propagation in solid media is described by a system of three strongly coupled hyperbolic equations with piece - wise constant coefitients. The characteristic set and hi-characteristic curves of this system are computed in a homogeneous half-space with free boundary and the formulae of reflection and diffraction of the hi-characteristics on the internal boundaries of the media. Applications of the characteristic set and bi-eharacteristic curves for the inverse problem in geophysics and Earth modelling are given.
文摘Aims and Scope The Journal of Computational Mathematics is published bi-monthly.It is an international journal covering all branches of modern computational mathematics such as numerical linear algebra,numerical optimization,computational geometry,numerical PDEs and inverse problems.Papers containing new ideas,creative approaches and/or innovative applications as well as invited reviews are expected to appear regularly in the journal.
基金Project supported by the Tianyuan Foundation of China.
文摘where U and F are the vector-valued functions which are defined on R<sup>+</sup>×R<sup>N</sup> and R<sup>+</sup>×R<sup>N</sup>×R<sup>N</sup>,respectively, U=（u<sub>1</sub>,…,u<sub>N</sub>）, F=（f<sub>1</sub>,…,f<sub>N</sub>）, =（<sub>x</sub><sub>1</sub>,……,<sub>x</sub>）<sub>N</sub>. Moreover, F is smooth enough, andits derivatives of all orders are boundary on R×K. K is any compact set in R<sup>2N</sup>.Obviously,
基金The work was supported by the National Natural Science Foundation of China （11271174）. The authors would like to thank the referees for the comments and constructive suggestions, which are valuable in improving the quality of the manuscript.
文摘In this paper, by exploiting the special block and sparse structure of the coefficient matrix, we present a new preconditioning strategy for solving large sparse linear systems arising in the time-dependent distributed control problem involving the heat equation with two different functions. First a natural order-reduction is performed, and then the reduced- order linear system of equations is solved by the preconditioned MINRES algorithm with a new preconditioning techniques. The spectral properties of the preconditioned matrix are analyzed. Numerical results demonstrate that the preconditioning strategy for solving the large sparse systems discretized from the time-dependent problems is more effective for a wide range of mesh sizes and the value of the regularization parameter.
