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Math. Comput. Appl. 2015, 20(2), 76-93; doi:10.3390/mca20010093

Shifted Jacobi Collocation Method Based on Operational Matrix for Solving the Systems of Fredholm and Volterra Integral Equations

Department of Applied Mathematics, Faculty of Mathematical Sciences Mohaghegh Ardabili University, Ardabil, Iran
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Published: 1 August 2015
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Abstract

This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product. The main aim is to generalize the Jacobi integral and product operational matrices to the solving system of Fredholm and Volterra equations. These matrices together with the collocation method are applied to reduce the solution of these problems to the solution of a system of algebraic equations. The method is applied to solve system of linear and nonlinear Fredholm and Volterra equations. Illustrative examples are included to demonstrate the validity and efficiency of the presented method. Also, several theorems, which are related to the convergence of the proposed method, will be presented.
Keywords: Collocation Method; Shifted Jacobi Polynomials; System of Fredholm and Volterra Integral Equations; Convergence; Operational Integral and Product Matrices Collocation Method; Shifted Jacobi Polynomials; System of Fredholm and Volterra Integral Equations; Convergence; Operational Integral and Product Matrices
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Borhanifar, A.; Sadri, K. Shifted Jacobi Collocation Method Based on Operational Matrix for Solving the Systems of Fredholm and Volterra Integral Equations. Math. Comput. Appl. 2015, 20, 76-93.

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