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

Chih Wen Chang, Chein Shan Liu, Jiang Ren Chang, Han Taw Chen

研究成果: Article同行評審

摘要

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.

原文English
頁(從 - 到)1653-1675
頁數23
期刊Inverse Problems in Science and Engineering
25
發行號11
DOIs
出版狀態Published - 2017 十一月 2

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Computer Science Applications
  • Applied Mathematics

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