﻿ 五阶偏微分方程的时间多区域时空谱方法

# 五阶偏微分方程的时间多区域时空谱方法Multi-Domain Space-Time Spectral Method in Time for Solving Fifth-Order Partial Differential Equation

Abstract: In this paper, we propose the multi-domain space-time spectral method in time for the fifth-order partial differential equation. Legendre-Petrov-Galerkin method is applied in space direction, and multi-domain Legendre-tau method is applied in time direction, that is: dividing the time interval into multiple domains and Legendre-tau method is applied in each domain. At the same time, the error analysis of the method on linear problems is given in this paper, and we choose proper basis functions to make the coefficient matrix sparse, the nonlinear term for the nonlinear equation is computed by interpolation through Chebyshev-Gauss-Lobatto points. Finally, some numerical examples are given to verify the effectiveness of the algorithm.

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