Comparative study of Three Numerical Schemes for Fractional Integro differential Equations

TL;DR

This paper compares three numerical schemes for solving fractional integro-differential equations with Caputo derivatives, analyzing their accuracy, error estimates, and performance through numerical tests.

Contribution

It provides a comparative analysis of Linear, Quadratic, and Quadratic-Linear schemes, including error estimates and performance evaluation for fractional equations.

Findings

All schemes perform well with increased terms.

Accuracy improves as step size decreases.

Performance varies among schemes based on problem specifics.

Abstract

This paper presents a comparative study 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 are increased, the desired solution is achieved. The accuracy of the numerical schemes with respect to the step size h is analyzed and illustrated through various tables. Finally, comparative performances of the schemes are discussed.