Derivation of a new semi-imlicit Runge-Kutta method of contra-harmonic mean with forward-backward technique

Jasim, Mahmood D.; Abduljabbar, Ammar Saad; Dahash, Noor Mawlood

doi:10.47974/JIM-2250

Open Access Research Article

Derivation of a new semi-imlicit Runge-Kutta method of contra-harmonic mean with forward-backward technique

^*Mahmood D. JasimCorresponding authormahoodalani@uomosul.edu.iq Mahmood.Al-Ani@univ-nantes.frAffiliation 1Department of MathematicsCollege of Basic EducationUniversity of MosulMosul, IraqAffiliation 2Jean Leray Laboratory of MathematicsUniversity of NantesFranceView full profile → , Ammar Saad Abduljabbarammarsaad86@uomosul.edu.iqDepartment of MathematicsCollege of Basic EducationUniversity of MosulMosul, IraqView full profile → , Noor Mawlood DahashNoor.mawlood@uomosul.edu.iqDepartment of MathematicsCollege of Basic EducationUniversity of MosulMosul, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 437–446Vol. 29Issue 2February 2026DOI: 10.47974/JIM-2250XML

Received:: 11 Mar 2025
Published Online:: 29 Jan 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2250
Pages:: 437–446

Abstract

In this article, the new method that solves Initial Value Problems IVPs is presented, where we derived our new method by using the Contra Harmonic CH mean instead of the classic arithmetic mean, more than the Forward Backward FB) technique to calculate both sides of the predictor (Forward) part and corrector (Backward) part of our semi-implicit method. The method was applied to a solved example with a different step size, and the results with the exact and the classical old method were compared with the old method.

Keywords

Initial value problems Implicit Runge-Kutta method Contra harmonic mean Forward backward technique Stability

Subject Classifications

65L0665L05

References

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