Extrapolation of Explicit DIMSIMs of High Order to Solve the Ordinary Differential Equations

Ali J. Kadhim, Annie Gorgey^*

Mathematics Department, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, Tanjong Malim, Perak, Malaysia.

DOI: 10.4236/jamp.2019.712212                

Abstract

The purpose of this research is to investigate the effciency of explicit diagonally implicit multi-stage integration methods with extrapolation. The author gave detailed explanation of explicit diagonally implicit multi-stage integration method and compared the base method with a technique known as extrapolation to improve the effciency. Extrapolation for symmetric Runge-Kutta method is proven to improve the accuracy since with extrapolation the solutions exhibit asymptotic error expansion, however for General linear methods, it is not known whether extrapolation can improve the effciency or not. Therefore this research focuses on the numerical experimental results of the explicit diagonally implicit multistage integration with and without extrapolation for solving some ordinary differential equations. The numerical results showed that the base method with extrapolation is more effcient than the method without extrapolation.

Keywords

Extrapolation Technique, General Linear Methods, Diagonally Implicit Muti-Stage Integration, Explicit Methods

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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