New multi-step Runge-Kutta method

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this article, a new class of Runge-Kutta methods for initial value problems y′ = f(x, y) are introduced, this method replace evaluations of f with approximations of f′ and use the harmonic mean in the main formula. If f′ is approximated to sufficient accuracy from past and current evaluations of f, the resulting multi-step Runge-Kutta method can be considered as replacing functional evaluations with approximations of f′. Here is presented an O(h3) method which requires only two evaluations of f. The stability of the method is analyzed. Numerical examples with excellent results are shown to verify that this new method is superior to existing multi-step method like the third order Adams-Bashforth.

Original languageEnglish
Pages (from-to)2255-2262
Number of pages8
JournalApplied Mathematical Sciences
Volume3
Issue number45-48
Publication statusPublished - 2009

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Multistep Methods
Runge Kutta methods
Runge-Kutta Methods
Initial value problems
Evaluation
Harmonic mean
Approximation
Evaluation Method
Initial Value Problem
Sufficient
Verify
Numerical Examples

Keywords

  • Harmonic mean
  • Multi-step Runge-Kutta
  • ODE solver
  • Third-order method

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

New multi-step Runge-Kutta method. / Ababneh, O. Y.; Ahmad, Rokiah @ Rozita; Ismail, Eddie Shahril.

In: Applied Mathematical Sciences, Vol. 3, No. 45-48, 2009, p. 2255-2262.

Research output: Contribution to journalArticle

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