Hybrid methods for direct integration of special third order ordinary differential equations

Y. D. Jikantoro, F. Ismail, N. Senu and Z.B. Ibrahim

Applied Mathematics and Computation, 2018, vol. 320, issue C, 452-463

Abstract: In this paper we present a new class of direct numerical integrators of hybrid type for special third order ordinary differential equations (ODEs), y′′′=f(x,y); namely, hybrid methods for solving third order ODEs directly (HMTD). Using the theory of B-series, order of convergence of the HMTD methods is investigated. The main result of the paper is a theorem that generates algebraic order conditions of the methods that are analogous to those of two-step hybrid method. A three-stage explicit HMTD is constructed. Results from numerical experiment suggest the superiority of the new method over several existing methods considered in the paper.

Keywords: Hybrid method; Three-step method; B-series; Order conditions; Third order ordinary differential equations; Numerical integrator (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:320:y:2018:i:c:p:452-463

DOI: 10.1016/j.amc.2017.10.003

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