一类带弱奇异核的偏积分微分方程的两种数值解

Two Numerical Solutions for a Partial Integro-differential Equation With a Weakly Singular Kernel

给出了数值求解一类偏微分方程的两种全离散格式。x方向一种采用Legendre谱方法,第二种采用Galerkin谱方法,t方向用拉普拉斯的数值逆求解。第二种方法更具有可操作性,精度高,便于理论分析的优点.

In this paper, two fully discrete methods of a partial integro - differential equation is con sidered.This article presents the Legendre spectral method and the Galerkin spectral method in the direction of x, but applies the inversion technique for the Laplace transform in the direction of t. The second method in more practical and more precise and easier to be analyzed theoretically.