An Overview of Iweobodo-Mamadu-Njoseh Wavelet (IMNW) and Its Steps in Solving Time Fractional Advection-Diffusion Problems
Iweobodo D. C *
Department of Mathematics, Dennis Osadebay University, Asaba, Delta State, Nigeria.
Njoseh I. N
Department of Mathematics, Delta State University, Abraka, Delta State, Nigeria.
Apanapudor J. S.
Department of Mathematics, Delta State University, Abraka, Delta State, Nigeria.
*Author to whom correspondence should be addressed.
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.
Keywords: Wavelets, Iweobodo-Mamadu-Njoseh Wavelet, Mamadu-Njoseh polynomials, weight functions, orthogonality and orthonormality, galerkin finite element technique