A direct variable step block multistep method for solving general third-order ODEs

Siamak Mehrkanoon*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

This paper discusses a direct three-point implicit block multistep method for direct solution of the general third-order initial value problems of ordinary differential equations using variable step size. The method is based on a pair of explicit and implicit of Adams type formulas which are implemented in PE(CE)t mode and in order to avoid calculating divided difference and integration coefficients all the coefficients are stored in the code. The method approximates the numerical solution at three equally spaced points simultaneously. The Gauss Seidel approach is used for the implementation of the proposed method. The local truncation error of the proposed scheme is studied. Numerical examples are given to illustrate the efficiency of the method.

Original languageEnglish
Pages (from-to)53-66
Number of pages14
JournalNumerical Algorithms
Volume57
Issue number1
DOIs
Publication statusPublished - May 2011

Keywords

  • Direct block method
  • Third-order ordinary differential equations
  • Three-point one-block
  • Variable step size

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