A Galerkin finite element technique with Iweobodo-Mamadu-Njoseh wavelet (IMNW) basis function for the solution of time-fractional advection–diffusion problems

Abstract

In this paper, the authors used wavelet-based Galerkin finite element technique constructed with Iweobodo-Mamadu-Njoseh wavelet as the basis function, for the numerical solution of time-fractional advection–diffusion equations. To achieve this, the authors used the Iweobodo-Mamadu-Njoseh wavelet as well as fractional calculus, wavelet and wavelet transform, and the Galerkin finite element technique. Also, time and space discretization in relation to the finite element technique were considered, followed by the steps in implementing numerical solutions to TFADE with the new technique. The new technique was considered in seeking numerical solutions of some Caputo type TFADE test problems, and the resulting numerical evidence displayed the effectiveness and accuracy of the method as the results obtained with the new method converged at a good pace to the exact solutions. The results obtained at different fractional order were also compared and the resulting evidence showed that at certain fractional value the convergence behavior displayed slight differences. Every numerical computation was done with the use of MAPLE 18 software.

Keywords

• Wavelets
• Iweobodo-Mamadu-Njoseh wavelet
• Mamadu-Njoseh polynomials
• Weight functions
• Orthogonality and orthonormality
• Galerkin finite element technique