Derivation and Implementation of a Fifth Stage Fourth Order Explicit Runge-Kutta Formula using 𝑓(𝑥,𝑦) Functional Derivatives
Esekhaigbe Aigbedion Christopher
Esekhaigbe Aigbedion Christopher, Department of Statistics, Federal Polytechnic, Auchi, Edo State, Nigeria.
Manuscript received on 16 February 2023 | Revised Manuscript received on 21 March 2023 | Manuscript Accepted on 15 April 2023 | Manuscript published on 30 December 2023 | PP: 28-32 | Volume-3 Issue-1, April 2023 | Retrieval Number: 100.1/ijam.A1144043123 | DOI: 10.54105/ijam.A1144.043123
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Abstract: This paper is aimed at using 𝒇(𝒙,𝒚) functional derivatives to derive a fifth stage fourth order Explicit Runge-Kutta formula for solving initial value problems in Ordinary Differential Equations. The 𝒇(𝒙,𝒚) functional derivatives from the general Runge-Kutta scheme will be compared with the 𝒇(𝒙,𝒚) functional derivatives from the Taylor series expansion to derive the method. The method will be implemented on some initial value problems, and results compared with results from the classical fourth order method. The results revealed that the method compared favorably well with the existing classical fourth order method.
Keywords: Initial Value Problems, Comparison, explicit, 𝒇(𝒙,𝒚) partial derivatives, Explicit Runge-Kutta Methods, Linear and non- linear equations, Taylor series expansion
Scope of the Article: Numerical Analysis