Modified Laguerre Spectral and Pseudospectral Methods for Nonlinear Partial Differential Equations in Multiple Dimensions

XU Cheng-long; GUO Ben-yu

Volume 29 Issue 3

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Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(3): 281-300

XU Cheng-long, GUO Ben-yu. Modified Laguerre Spectral and Pseudospectral Methods for Nonlinear Partial Differential Equations in Multiple Dimensions[J]. Applied Mathematics and Mechanics, 2008, 29(3): 281-300.

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Modified Laguerre Spectral and Pseudospectral Methods for Nonlinear Partial Differential Equations in Multiple Dimensions

XU Cheng-long^1,2,
GUO Ben-yu^2,3,4

1.
Department of Mathematics, Tongji University, Shanghai 200092, P. R. China;

Received Date: 2007-12-12
Rev Recd Date: 2008-01-24
Publish Date: 2008-03-15

Abstract

Abstract

The Laguerre spectral and pseudospectral methods for multiple-dimensional nonlinear partial differential equations are investigated. Some results on the modified Laguerre orthogonal approximation and interpolation were established, which play important roles in the related numerical methods for unbounded domains. As an example, the modified Laguerre spectral and pseudospectral methods were proposed for two-dimensional Logistic equation. The stability and convergence of suggested schemes were proved. Numerical results demonstrate the high accuracy of these approaches.

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References

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