$C^{3}$-spline Methods for Solving Fractional Integro-differential Equations

Document Type : Original Article

Authors

1 Department of Mathematics‎, ‎Karaj Branch‎, ‎Islamic Azad University‎, ‎Karaj 31499-68111

2 Iran University of Science and Technology

3 3Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj

Abstract

Fractional integro-differential equations (FIDEs) constitute an important mathematical tool in modeling many dynamical processes‎. ‎To solve FIDEs‎, ‎several analytical and numerical methods have been proposed‎, ‎namely those based on symmetry and spline approaches‎. ‎This paper proposes quartic and sextic C3-spline methods for the numerical solution of FIDEs‎. ‎The convergence analysis of the proposed strategy is examined in detail‎. ‎Finally‎, ‎three numerical examples are given to illustrate the numerical accuracy and efficiency of the proposed strategy‎.

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