摘要
以半线性抛物方程为例,对交替方向隐式(ADI)迭代法进行了改进,改进的ADI迭代法通过求解较低维数的矩阵方程,降低了程序实现难度,大大减少了计算量,并将其应用到求解半线性椭圆方程,改进的ADI迭代法可以作为通用求解器去解椭圆方程和抛物方程.数值算例验证了改进的ADI迭代法的优越性.
In the paper, we proposed a modified ADI iterative method, which can reduce the difficulty and complexity of the calculation process by solving the lower dimension matrix equations in each iterative step. In addition, we also gave the comparison between modified ADI iterative method with the classical ADI iterative method. Finally, we gave the numerical experiments to verify the advantage of the modified ADI iterative method.
作者
葛志昊
刘富豪
王慧芳
GE Zhihao;LIU Fuhao;WANG Huifang(Henan University a.School of Mathematics and Statistic;Institute of Applied Mathematics,Henan Kaifeng 475004,China)
出处
《河南大学学报（自然科学版）》
CAS
2018年第4期485-491,共7页
Journal of Henan University:Natural Science
基金
河南省自然科学基金项目(162300410031)
河南大学优秀青年资助项目(yqpy20140039)
关键词
半线性抛物方程
ADI迭代法
矩阵方程
semi-linear parabolic equation
ADI iterative method
matrix equation
