Development and Implementation of Block Unification Multi-step Methods for the Solution of Second Order Ordinary Differential Equations

Umaru Mohammed, Oyelami Oyewole, Mikhail Semenov, Aliyu Ma'Ali

Research output: Contribution to journalConference articlepeer-review

Abstract

In this paper, linear multi-step hybrid block methods with three-, four- and five-step numbers are developed for approximating directly the solution of second order Initial and Boundary Value Problems (IBVPs). Multiple finite difference formulas are derived and combined in a block formulation to form a numerical integrator that provides direct solution to second order IBVPs over sub-intervals. A new class of orthogonal polynomials constructed as basis function to develop the hybrid block methods adopting collocation technique with a non-negative weight function. The scheme is applied as simultaneous integrator to second order initial value and boundary value problems of ODEs. The properties and convergence of the proposed method are discussed. The derived schemes were used to solve some problems and the numerical result shows the effectiveness, accuracy and superiority of the method over the existing methods found in the literature.

Original languageEnglish
Article number012088
JournalJournal of Physics: Conference Series
Volume1366
Issue number1
DOIs
Publication statusPublished - 7 Nov 2019
Event2nd International Conference on Applied and Industrial Mathematics and Statistics 2019, ICoAIMS 2019 - Kuantan, Pahang, Malaysia
Duration: 23 Jul 201925 Jul 2019

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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