Numerical solutions of fifth order boundary value problems using Mamadu-Njoseh polynomials

Abstract

Mamadu-Njoseh polynomials are polynomials constructed in the interval [-1,1] with respect to the weight function ?(?) = ?² + 1. This paper aims at applying these polynomials, as trial functions satisfying the boundary conditions, in a numerical
approach for the solution of fifth order boundary value problems. For this, these polynomials map the interval [0,1] to the interval [-1,1] bijectively, implying these polynomials are orthogonal in [0,1]. Numerical experiments are performed for both linear and nonlinear boundary value problems to verify the accuracy of the proposed method. Results obtained are compared with those of B-spline function method available in the literature.

Keywords: Boundary value problem, Orthogonality, Bijective mapping, Mamadu-Njoseh Polynomials, Approximate solution