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.
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 *