Jacobi Operational Matrix Approach for Solving Systems of Linear and Nonlinear Integro-Differential Equations

Subject Areas : International Journal of Mathematical Modelling & Computations

Khadijeh Sadri ¹ , Zainab Ayati ²

1 - Guilan University
2 - Department of Engineerig Sciences‎, ‎Faculty of Technology and Engineering East of Guilan

Received: 2016-10-07 Accepted : 2017-01-13 Published : 2017-01-01

Keywords: collocation method, Shifted Jacobi polynomials, System of Fredholm and Volterra integro-differential equations, Operational matrices of integration and product, &lrm, Convergence,

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 integro--differential equations‎ which appear in various fields of science such as physics and engineering. ‎The Operational matrices together with the collocation method are applied to reduce the solution of these problems to the solution of a system of algebraic equations‎. ‎ Indeed, to solve the system of integro-differential equations, a fast algorithm is used for simplifying the problem under study. ‎The method is applied to solve system of linear and nonlinear Fredholm and Volterra integro-differential equations‎. ‎Illustrative examples are included to demonstrate the validity and efficiency of the presented method‎. It is further found that the absolute errors are almost constant in the studied interval. ‎Also‎, ‎several theorems related to the convergence of the proposed method‎, ‎will be presented‎‎.‎