Shifted Jacobi spectral collocation method with convergence analysis for solving integro-differential equations and system of integro-differential equations

Abstract

This article addresses the solution of multi-dimensional integro-differential equations (IDEs) by means of the spectral collocation method and taking the advantage of the properties of shifted Jacobi polynomials. The applicability and accuracy of the present technique have been examined by the given numerical examples in this paper. By means of these numerical examples, we ensure that the present technique is simple and very accurate. Furthermore, an error analysis is performed to verify the correctness and feasibility of the proposed method when solving IDE.

New Results of Some of the Conformable Models Arising in Dynamical Systems

“…Numerous mathematical procedures have been presented to get results of NLCMs, for example, homotopy perturbation method [1], residual power series method [2], Shifted Jacobi spectral collocation method [3], reproducing kernel Hilbert space method [4], modified generalized Taylor fractional series method [5], the improved fractional Riccati extension scheme [6], method of separation variables [7], generalized ðG′/GÞ -extension scheme [8], Chebyshev collocation way [9], rational ðG′/GÞ-extension scheme [10], the first integral way [11], modified exp-task way [12], variational iteration method [13], modified Khater method [14], and iterative reproducing kernel Hilbert space approach [15].…”

A new difference method for the singularly perturbed Volterra-Fredholm integro-differential equations on a Shishkin mesh

“…Orthonormal Bernstein and Block Pulse functions method were presented in [35]. Shifted Jacobi spectral collocation method was performed to multi-dimensional VFIDEs in [10]. Nyström discretization approach was introduced in [13].…”

Accurate spectral algorithm for two‐dimensional variable‐order fractional percolation equations

“…The local methods compute the solutions at particular points; in contrast, the global ones obtain the solutions overall the problem domain 6,7 . For example, the finite element and finite difference methods are local, 8‐13 while the spectral methods are global 14‐18 . The spectral methods gained importance due to their high convergence speed, accuracy, and applicability to either bounded or unbounded domains 16‐19 .…”