A simple spatial integration scheme for solving Cauchy problems of non-linear evolution equations. Issue 11 (2nd November 2017)

• Record Type: Journal Article
• Authors: Chang, Chih-Wen; Liu, Chein-Shan; Chang, Jiang-Ren; Chen, Han-Taw
• Is Part Of: Inverse problems in science and engineering. Volume 25:Issue 11(2017)
• Page Start: 1653
• Page End: 1675
• Publication Date: 2017-11-02
• Subjects: Non-linear evolution equation -- severely ill-posed problem -- Cauchy problem -- group preserving scheme (GPS) -- without initial condition; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2017.1281271
• Languages: English
• ISSNs: 1741-5977

Abstract

Abstract: 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.