Pell Collocation Pseudo Spectral Scheme for One-Dimensional Time-Fractional Convection Equation with Error Analysis

Abstract

In the current manuscript, we implement the collocation method to obtain an approximate solution of one-dimensional time-fractional convection equation. The operational matrices of Pell polynomials are applied to solve the fractional partial differential equations. In the Caputo sense, we describe the time-fractional derivatives. So, this algorithm allows us to transform the fractional differential equation with initial (boundary) conditions into a system of algebraic equations in a good form. The convergence and error analysis of Pell polynomials are carefully investigated, and some examples are explored to show the comparison and efficiency of our method with others.