Convergence of the L1 Two-Term Equation Scheme

Abstract

Fractional derivatives have found application in modeling various processes in different fields of science. Finite difference schemes are a main approach for numerical solution of models using fractional differential equations. In this paper we investigate the convergence and order of the numerical solution of two-term ordinary fractional differential equation which uses the L1 approximation of the fractional derivative. Inequalities for the weights of L1 approximation are derived and used to prove the convergence of the L1 scheme for the two-term equation. Conditions for the parameter of the two-term equation and error estimates of L1 scheme are obtained. Experimental results for the order and error of the L1 scheme are presented in the paper.