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

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)1653-1675
Number of pages23
JournalInverse Problems in Science and Engineering
Volume25
Issue number11
DOIs
Publication statusPublished - 2017 Nov 2

Fingerprint

Nonlinear Evolution Equations
Ordinary differential equations
Cauchy Problem
Semidiscretization
Discretization Scheme
Ill-posed Problem
Numerical Scheme
Ordinary differential equation
Experiments
Integrate
Numerical Experiment

All Science Journal Classification (ASJC) codes

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

Cite this

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A simple spatial integration scheme for solving Cauchy problems of non-linear evolution equations. / Chang, Chih Wen; Liu, Chein Shan; Chang, Jiang Ren; Chen, Han-Taw.

In: Inverse Problems in Science and Engineering, Vol. 25, No. 11, 02.11.2017, p. 1653-1675.

Research output: Contribution to journalArticle

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