Perturbation by Decomposition:A New Approach to Singular Initial Value Problems with Mamadu-Njoseh Polynomials as Basis Functions

• 作者: Mamadu E.J. Tsetimi J.
• 来源期刊: 数学和系统科学:英文版
• 学科: 数学
• 关键词: Perturbation method Orthogonal polynomials Mamadu-Njoseh polynomials Chebychev polynomials singular initial value problems ordinary differential equation(ODE)
• 年，卷（期）: 2020,（1）
• 页码范围: 15-18
• 页数: 4页
• 分类号: O17

摘要

This paper focuses on the application of Mamadu-Njoseh polynomials(MNPs)as basis functions for the solution of singular initial value problems in the second-order ordinary differential equations in a perturbation by decomposition approach.Here,the proposed method is an hybrid of the perturbation theory and decomposition method.In this approach,the approximate solution is slihtly perturbed with the MNPs to ensure absolute convergence.Nonlinear cases are first treated by decomposition.The method is,easy to execute with well-posed mathematical formulae.The existence and convergence of the method is also presented explicitly.Resulting numerical evidences show that the proposed method,in comparison with the Adomian Decomposition Method(ADM),Homotpy Pertubation Method and the exact solution is reliable,efficient and accuarate.