An Overview of Iweobodo-Mamadu-Njoseh Wavelet (IMNW) and Its Steps in Solving Time Fractional Advection-Diffusion Problems

Abstract

This paper revisited the newly constructed wavelet-based Galerkin finite element technique by Iweobodo et al (2023) and reiterated the steps in seeking approximate solutions to time-fractional advection -diffusion problems with the method. Orthogonal polynomials, Mamadu-Njoseh polynomials and finite element method were discussed in relation to Iweobodo-Mamadu-Njoseh wavelet (IMNW) and the step-by-step application of the wavelet-based Galerkin finite element technique using the (IMNW) as a basis function was iterated. It was easy to achieve a system of linear equations which is solved for the unknown parameters. Also, a convergence investigation of the IMNW wavelet-based Galerkin finite element technique was undertaken, and the resulting evidence exhibited uniformity in convergence.