SOLUTION TO FRACTIONAL ORDER ADVECTION-DISPERSION PROBLEMS USING GALERKIN METHOD WITH MAMADU-NJOSEH POLYNOMIALS

Abstract

The advection-dispersion equation is a partial differential equation describing a probability function for the location of particles in continuum. Finding the analytic solution to this equation is very difficult and cumbersome. Thus, in this research, we have considered the numerical approximation of fractional time and space advection-dispersion equation. Specifically, Galerkin Method was adopted as the numerical method with Mamadu-Njoseh polynomials as basis functions to obtain the approximate solution of the fractional adventure-dispersion equation. The study established that the Galerkin method effectively solves fractional order advection-dispersion equation with time and space derivatives and that the method converges rapidly with an increase in the value of the fractional order ????, for ???? = 0.1. The numerical results obtained show that the method converges rapidly to the exact solution