Multistage optimal homotopy asymptotic method for solving initial-value problems

N. R. Anakira, A. K. Alomari, A. F. Jameel, Ishak Hashim

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper, a new approximate analytical algorithm namely multistage optimal homotopy asymptotic method (MOHAM) is presented for the first time to obtain approximate analytical solutions for linear, nonlinear and system of initial value problems (IVPs). This algorithm depends on the standard optimal homotopy asymptotic method (OHAM), in which it is treated as an algorithm in a sequence of subinterval. The main advantage of this study is to obtain continuous approximate analytical solutions for a long time span. Numerical examples are tested to highlight the important features of the new algorithm. Comparison of the MOHAM results, standard OHAM, available exact solution and the fourth-order Runge Kutta (RK4) reveale that this algorithm is effective, simple and more impressive than the standard OHAM for solving IVPs.

Original languageEnglish
Pages (from-to)1826-1843
Number of pages18
JournalJournal of Nonlinear Science and Applications
Volume9
Issue number4
Publication statusPublished - 2016

Fingerprint

Homotopy Method
Asymptotic Methods
Initial Value Problem
Analytical Solution
Runge-Kutta
Fourth Order
Exact Solution
Numerical Examples
Standards

Keywords

  • Initial value problems
  • Mathematica 9
  • Multistage optimal homotopy asymptotic method (MOHAM)
  • Optimal homotopy asymptotic method (OHAM)
  • Series solution

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis

Cite this

Multistage optimal homotopy asymptotic method for solving initial-value problems. / Anakira, N. R.; Alomari, A. K.; Jameel, A. F.; Hashim, Ishak.

In: Journal of Nonlinear Science and Applications, Vol. 9, No. 4, 2016, p. 1826-1843.

Research output: Contribution to journalArticle

Anakira, N. R. ; Alomari, A. K. ; Jameel, A. F. ; Hashim, Ishak. / Multistage optimal homotopy asymptotic method for solving initial-value problems. In: Journal of Nonlinear Science and Applications. 2016 ; Vol. 9, No. 4. pp. 1826-1843.
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