A new class of orthogonal polynomials as trial function for the derivation of numerical integrators
Department of Mathematical Sciences, Bingham University Karu, Nigeria.
Research Article
GSC Advanced Research and Reviews, 2022, 12(03), 001–012.
Article DOI: 10.30574/gscarr.2022.12.3.0229
Publication history:
Received on 26 July 2022; revised on 30 August 2022; accepted on 01 September 2022
Abstract:
This paper presents a set of newly constructed polynomials valid in interval [-1, 1] with respect to weight function w(x) = x + 1. For applicability sake, the polynomials shall be employed as trial function to develop a fast, efficient and reliable block algorithm for the numerical solution of ordinary differential equations with application to second order initial value problems. Collocation and interpolation techniques were adopted for the formulation of self-starting continuous hybrid schemes. Findings from the analysis of the basic properties of the method using appropriate existing theorems show that the developed schemes are consistent, zero-stable and hence convergent. On implementation, the superiority of the scheme over the existing method is established numerically. Further investigation of the properties of these polynomials is ongoing as we hope to discuss this in the future paper.
Keywords:
Collocation; Interpolation; Orthogonal polynomials; Block method; Hybrid
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Copyright © 2022 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution Liscense 4.0
