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

International Journal of Mathematical Modelling & Computations

مقاله 1، دوره 7، 1 (WINTER) - شماره پیاپی 25، فروردین 2017، صفحه 1-25   

نوع مقاله: Full Length Article

نویسندگان

Khadijeh Sadri^{* 1}؛ Zainab Ayati²

¹Guilan University

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

چکیده

‎‎‎‎‎‎‎‎‎‎‎‎‎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.‎

کلیدواژه‌ها

collocation method؛ Shifted Jacobi polynomials؛ System of Fredholm and Volterra integro-differential equations؛ Operational matrices of integration and product؛ ‎Convergence