In this paper we describe a new pseudo-spectral method to solve numerically two and three-dimensional nonlinear diffusion equations over unbounded domains,taking Hermite functions,sinc functions,and rational Chebyshev...In this paper we describe a new pseudo-spectral method to solve numerically two and three-dimensional nonlinear diffusion equations over unbounded domains,taking Hermite functions,sinc functions,and rational Chebyshev polynomials as basis functions.The idea is to discretize the equations by means of differentiation matrices and to relate them to Sylvester-type equations by means of a fourth-order implicit-explicit scheme,being of particular interest the treatment of three-dimensional Sylvester equations that we make.The resulting method is easy to understand and express,and can be implemented in a transparent way by means of a few lines of code.We test numerically the three choices of basis functions,showing the convenience of this new approach,especially when rational Chebyshev polynomials are considered.展开更多
Presents a study that determined a theoretical proof for the spectral analysis result of the first-order Hermite cubic spline collocation differentation matrices. Background on the Hermite cubic spline collocation met...Presents a study that determined a theoretical proof for the spectral analysis result of the first-order Hermite cubic spline collocation differentation matrices. Background on the Hermite cubic spline collocation method; Basis of the argumentation in the study regarding the condensation technique and the Hurwitz theorem; Numerical results.展开更多
文摘In this paper we describe a new pseudo-spectral method to solve numerically two and three-dimensional nonlinear diffusion equations over unbounded domains,taking Hermite functions,sinc functions,and rational Chebyshev polynomials as basis functions.The idea is to discretize the equations by means of differentiation matrices and to relate them to Sylvester-type equations by means of a fourth-order implicit-explicit scheme,being of particular interest the treatment of three-dimensional Sylvester equations that we make.The resulting method is easy to understand and express,and can be implemented in a transparent way by means of a few lines of code.We test numerically the three choices of basis functions,showing the convenience of this new approach,especially when rational Chebyshev polynomials are considered.
基金The Project supported by A Grant from the Research Grants Council of the Hong Kong Spelial Administrative Region, China (Project No. CityU 1061/00p) the Foundation of Chinese Academy of Engineering Physics.
文摘Presents a study that determined a theoretical proof for the spectral analysis result of the first-order Hermite cubic spline collocation differentation matrices. Background on the Hermite cubic spline collocation method; Basis of the argumentation in the study regarding the condensation technique and the Hurwitz theorem; Numerical results.
