A simple spatial integration scheme for solving Cauchy problems of non-linear evolution equations

作者：Chang, Chih-Wen^*; Liu, Chein-Shan; Chang, Jiang-Ren; Chen, Han-Taw

来源：Inverse Problems in Science and Engineering, 2017, 25(11): 1653-1675.

DOI：10.1080/17415977.2017.1281271

• Non-linear evolution equation
• severely ill-posed problem
• Cauchy problem
• group preserving scheme (GPS)
• without initial condition

In this study, we address a new and simple non-iterative method to solve Cauchy problems of non-linear evolution equations without initial data. To start with, these ill-posed problems are analysed by utilizing a semi-discretization numerical scheme. Then, the resulting ordinary differential equations at the discretized times are numerically integrated towards the spatial direction by the group-preserving scheme (GPS). After that, we apply a two-stage GPS to integrate the semi-discretized equations. We reveal that the accuracy and stability of the new approach is very good from several numerical experiments even under a large random noisy effect and a very large time span.

• 出版日期2017
• 单位河海大学