Comparative study of three numerical schemes for fractional integro-differential equations

Abstract

This paper presents a comparative study of three numerical schemes such as Linear, Quadratic and Quadratic–Linear scheme for the fractional integro-differential equations defined in terms of the Caputo fractional derivatives. The error estimates of the respective approximations are also established. Numerical tests of the discussed schemes show that all schemes work well, and when the number of terms approximating the solution is increased, the desired solution is achieved. The accuracy of the numerical schemes with respect to the step size h is analysed and illustrated through various tables. Finally, comparative performances of the schemes are discussed. © 2016 Elsevier B.V.