Title: Approximate solution of a fifth order ordinary differential equations with block method

Authors: Saumya Ranjan Jena; Guesh Simretab Gebremedhin

Addresses: Department of Mathematics, School of Applied Sciences, KIIT DT University, Bhubaneswar, 751024, Odisha, India ' Department of Mathematics, School of Applied Sciences, KIIT DT University, Bhubaneswar, 751024, Odisha, India

Abstract: In this paper an eighth step block method has been developed to obtain the approximate solution of an initial value problem involving fifth order ordinary differential equations. The derivation of the eight step block method is performed by collocation and interpolation approaches. The efficiency of an eighth step block method is illustrated by four numerical examples and comparison of the new method has been made with ODE45, LMM and analytical solutions. Stability and convergence analysis are discussed. The method is useful for solving fifth order ODEs arising in various physical problems.

Keywords: block method; initial value problems; Taylor series; stability.

DOI: 10.1504/IJCSM.2020.112652

International Journal of Computing Science and Mathematics, 2020 Vol.12 No.4, pp.413 - 426

Received: 23 Jan 2018
Accepted: 27 Aug 2018
Published online: 26 Jan 2021 *

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