Modified Hybrid Method with Four Stages for Second Order Ordinary Differential Equations

Faieza Samat and Eddie Shahril Ismail
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Faieza Samat: GENIUS@Pintar National Gifted Centre, Universiti Kebangsaan Malaysia, Selangor 43600, Malaysia
Eddie Shahril Ismail: Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Selangor 43600, Malaysia

Mathematics, 2021, vol. 9, issue 9, 1-7

Abstract: A modified explicit hybrid method with four stages is presented, with the first stage exactly integrating exp( wx ), while the remaining stages exactly integrate sin( wx ) and cos( wx ). Special attention is paid to the phase properties of the method during the process of parameter selection. Numerical comparisons of the proposed and existing hybrid methods for several second-order problems show that the proposed method gives high accuracy in solving the Duffing equation and Kramarz’s system.

Keywords: hybrid method; variable coefficients; second-order ordinary differential equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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