Legendre Collocation Method for Generalized Fractional Advection Diffusion Equation

Abstract

In this chapter, the collocation method is extended for a new class of fractional advection diffusion equation (GFADE). The GFADE is defined in terms of the generalized fractional derivatives(GFD) using scale and weight functions. The numerical solution of such GFADE is derived via a collocation method using Legendre polynomials. Convergence and error analysis of polynomial approximation are obtained. Numerical examples with homogeneous and nonhomogeneous boundary conditions are presented to confirm the theoretical findings. Through comparative study of the simulation results, we find that our proposed numerical method is simple, efficient and easy to implement. © 2023 Taylor & Francis Group, LLC.