In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and ...In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and the system of Hirota-Satsuma coupled KdV. In addition, the results obtained from Laplace decomposition method (LDM) and Pade approximant are compared with corresponding exact analytical solutions.展开更多
A barrier option valuation model with stochastic barrier which was regarded as the main feature of the model was developed under the Hull-White interest rate model.The purpose of this study was to deal with the stocha...A barrier option valuation model with stochastic barrier which was regarded as the main feature of the model was developed under the Hull-White interest rate model.The purpose of this study was to deal with the stochastic barrier by means of partial differential equation methods and then derive the exact analytical solutions of the barrier options.Furthermore,a numerical example was given to show how to apply this model to pricing one structured product in realistic market.Therefore,this model can provide new insight for future research on structured products involving barrier options.展开更多
In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging, scientific computing, reverse engineering and geometric modelling. Th...In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging, scientific computing, reverse engineering and geometric modelling. The reconstructed surface is obtained by continuously deforming an initial surface following the Partial Differential Equation (PDE)-based diffusion model derived by a minimal volume-like variational formulation. The evolution is driven both by the distance from the data set and by the curvature analytically computed by it. The distance function is computed by implicit local interpolants defined in terms of radial basis functions. Space discretization of the PDE model is obtained by finite co-volume schemes and semi-implicit approach is used in time/scale. The use of a level set method for the numerical computation of the surface reconstruction allows us to handle complex geometry and even changing topology,without the need of user-interaction. Numerical examples demonstrate the ability of the proposed method to produce high quality reconstructions. Moreover, we show the effectiveness of the new approach to solve hole filling problems and Boolean operations between different data sets.展开更多
In this paper, we study the fractional-order biological population models （FI3PMs） with Malthusian~ Verhulst, and porous media laws. The fractional derivative is defined in Caputo sense. The optimal homotopy asympto...In this paper, we study the fractional-order biological population models （FI3PMs） with Malthusian~ Verhulst, and porous media laws. The fractional derivative is defined in Caputo sense. The optimal homotopy asymptotic method （OHAM） for partial differ- ential equations （PDEs） is extended and successfully implemented to solve FBPMs. Third-order approximate solutions are obtained and compared with the exact solutions. The numerical results unveil that the proposed extension in the OHAM for fractional- order differential problems is very effective and simple in computation. The results reveal the effectiveness with high accuracy and extremely efficient to handle most complicated biological population models.展开更多
The aim of this paper is to present the backward substitution method for solving a class of fractional dual-phase-lag models of heat transfer.The proposed method is based on the Fourier series expansion along the spat...The aim of this paper is to present the backward substitution method for solving a class of fractional dual-phase-lag models of heat transfer.The proposed method is based on the Fourier series expansion along the spatial coordinate over the orthonormal basis formed by the eigenfunctions of the corresponding Sturm-Liouville problem.This Fourier expansion of the solution transforms the original fractional par-tial differential equation into a sequence of multi-term fractional ordinary differential equations.These fractional equations are solved by the use of the backward substi-tution method.The numerical examples with temperature-jump boundary condition and parameters of the tissue confirm the high accuracy and efficiency of the proposed numerical scheme.展开更多
This paper is concerned with a low-dimensional dynamical system model for analytically solving partial differential equations(PDEs).The model proposed is based on a posterior optimal truncated weighted residue(POT-WR)...This paper is concerned with a low-dimensional dynamical system model for analytically solving partial differential equations(PDEs).The model proposed is based on a posterior optimal truncated weighted residue(POT-WR)method,by which an infinite dimensional PDE is optimally truncated and analytically solved in required condition of accuracy.To end that,a POT-WR condition for PDE under consideration is used as a dynamically optimal control criterion with the solving process.A set of bases needs to be constructed without any reference database in order to establish a space to describe low-dimensional dynamical system that is required.The Lagrangian multiplier is introduced to release the constraints due to the Galerkin projection,and a penalty function is also employed to remove the orthogonal constraints.According to the extreme principle,a set of ordinary differential equations is thus obtained by taking the variational operation of the generalized optimal function.A conjugate gradient algorithm by FORTRAN code is developed to solve the ordinary differential equations.The two examples of one-dimensional heat transfer equation and nonlinear Burgers’equation show that the analytical results on the method proposed are good agreement with the numerical simulations and analytical solutions in references,and the dominant characteristics of the dynamics are well captured in case of few bases used only.展开更多
文摘In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and the system of Hirota-Satsuma coupled KdV. In addition, the results obtained from Laplace decomposition method (LDM) and Pade approximant are compared with corresponding exact analytical solutions.
基金National Natural Science Foundations of China(Nos.11471175,11171221)
文摘A barrier option valuation model with stochastic barrier which was regarded as the main feature of the model was developed under the Hull-White interest rate model.The purpose of this study was to deal with the stochastic barrier by means of partial differential equation methods and then derive the exact analytical solutions of the barrier options.Furthermore,a numerical example was given to show how to apply this model to pricing one structured product in realistic market.Therefore,this model can provide new insight for future research on structured products involving barrier options.
基金supported by PRIN-MIUR-Cofin 2006,project,by"Progetti Strategici EF2006"University of Bologna,and by University of Bologna"Funds for selected research topics"
文摘In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging, scientific computing, reverse engineering and geometric modelling. The reconstructed surface is obtained by continuously deforming an initial surface following the Partial Differential Equation (PDE)-based diffusion model derived by a minimal volume-like variational formulation. The evolution is driven both by the distance from the data set and by the curvature analytically computed by it. The distance function is computed by implicit local interpolants defined in terms of radial basis functions. Space discretization of the PDE model is obtained by finite co-volume schemes and semi-implicit approach is used in time/scale. The use of a level set method for the numerical computation of the surface reconstruction allows us to handle complex geometry and even changing topology,without the need of user-interaction. Numerical examples demonstrate the ability of the proposed method to produce high quality reconstructions. Moreover, we show the effectiveness of the new approach to solve hole filling problems and Boolean operations between different data sets.
文摘In this paper, we study the fractional-order biological population models （FI3PMs） with Malthusian~ Verhulst, and porous media laws. The fractional derivative is defined in Caputo sense. The optimal homotopy asymptotic method （OHAM） for partial differ- ential equations （PDEs） is extended and successfully implemented to solve FBPMs. Third-order approximate solutions are obtained and compared with the exact solutions. The numerical results unveil that the proposed extension in the OHAM for fractional- order differential problems is very effective and simple in computation. The results reveal the effectiveness with high accuracy and extremely efficient to handle most complicated biological population models.
基金The work was supported by the Natural Science Foundation of China(No.12072103)the Fundamental Research Funds for the Central Universities(No.B200202126)+4 种基金the Natural Science Foundation of Jiangsu Province(No.BK20190073)the State Key Laboratory of Acoustics,Chinese Academy of Sciences(No.SKLA202001)the State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University(No.KF2020-22)the Key Laboratory of Intelligent Materials and Structural Mechanics of Hebei Province(No.KF2021-01)the China Postdoctoral Science Foundation(Nos.2017M611669 and 2018T110430).
文摘The aim of this paper is to present the backward substitution method for solving a class of fractional dual-phase-lag models of heat transfer.The proposed method is based on the Fourier series expansion along the spatial coordinate over the orthonormal basis formed by the eigenfunctions of the corresponding Sturm-Liouville problem.This Fourier expansion of the solution transforms the original fractional par-tial differential equation into a sequence of multi-term fractional ordinary differential equations.These fractional equations are solved by the use of the backward substi-tution method.The numerical examples with temperature-jump boundary condition and parameters of the tissue confirm the high accuracy and efficiency of the proposed numerical scheme.
基金supported by Natural Science Foundation of China under Great Nos.11072053 and 11372068,and the National Basic Research Program of China under Grant No.2014CB74410.
文摘This paper is concerned with a low-dimensional dynamical system model for analytically solving partial differential equations(PDEs).The model proposed is based on a posterior optimal truncated weighted residue(POT-WR)method,by which an infinite dimensional PDE is optimally truncated and analytically solved in required condition of accuracy.To end that,a POT-WR condition for PDE under consideration is used as a dynamically optimal control criterion with the solving process.A set of bases needs to be constructed without any reference database in order to establish a space to describe low-dimensional dynamical system that is required.The Lagrangian multiplier is introduced to release the constraints due to the Galerkin projection,and a penalty function is also employed to remove the orthogonal constraints.According to the extreme principle,a set of ordinary differential equations is thus obtained by taking the variational operation of the generalized optimal function.A conjugate gradient algorithm by FORTRAN code is developed to solve the ordinary differential equations.The two examples of one-dimensional heat transfer equation and nonlinear Burgers’equation show that the analytical results on the method proposed are good agreement with the numerical simulations and analytical solutions in references,and the dominant characteristics of the dynamics are well captured in case of few bases used only.
