Convergence Analysis of the Collocation Method for Solving Two-dimensional Fractional Volterra Integro-differential Equations

Abstract

The collocation method is one of the well-known numerical methods to solve different kinds of differential and integral equations, which has attracted the attention of many researchers in recent years. In Kazemi and Tari (Iran J Sci Technol Trans A Sci 46:1629–1639, 2022), the collocation method was extended to solve two-dimensional fractional Volterra integro-differential equations (2D-FVIDEs). In the current paper, which is a continuation of the mentioned work, the error and convergence analysis of it is investigated. Here, the existence and uniqueness of the solution are proved and a resolvent kernel representation is given to the solution. Then, the convergence of the method is proved in a theorem which also gives the convergence order. Finally, some numerical examples are given to confirm the theoretical results.