交替方向Galerkin方法在偏积分微分方程中的应用

Application of Alternating Direction Galerkin Method in Partial Integral Differential Equation

用交替方向Galerkin方法研究二维带有弱奇异核的偏积分微分方程的数值解,在空间方向上,采用线性有限元,时间方向上采用向后欧拉方法,积分项用一阶卷积求积逼近,该方法既具有交替方向存储量少,计算量低,又具有有限元高精度的特点.

Alternating direction implicit Galerkin method are formulated for the two-dimensional partial intergro-differential equations with a weakly singular kernel. These techniques are based on the finite element method in space and the backward Euler in time in combination with order one convolution quadrature approximating the integral term. The method has not only less storage and low computational characteristics, but also has high precision characteristics with finite element method.