Consistency and Convergence Analysis of an 𝐹(𝑥,𝑦) Functionally Derived Explicit Fifth-Stage Fourth-Order Runge-Kutta Method
Esekhaigbe Aigbedion Christopher

Dr. Esekhaigbe Aigbedion Christopher, Department of Statistics, Federal Polytechnic, Auchi, Edo State, Nigeria.

Manuscript received on 16 February 2023 | Revised Manuscript received on 06 December 2023 | Manuscript Accepted on 15 December 2023 | Manuscript published on 30 December 2023 | PP: 10-12 | Volume-10 Issue-4, December 2023 | Retrieval Number: 100.1/ijbsac.A1145043123 | DOI: 10.35940/ijbsac.A1145.1210423

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Abstract: The purpose of this paper is to analyze the consistency and convergence of an explicit fifth-stage fourth-order Runge-Kutta method derived using 𝒇(𝒙,𝒚) functional derivatives. The analysis revealed that the method is consistent and convergent. The implementation of this method on initial-value problems was done in a previous paper, and it revealed that the method compared favorably well with the existing classical fourth stage fourth order explicit Runge Kutta method.

Keywords: Consistency, Convergence, Explicit, Runge-Kutta Methods, Linear and non- linear equations, Taylor series, Parameters, Initial-value Problems, 𝒇(𝒙,𝒚) functional derivatives.
Scope of the Article: Statistics