- Cankaya University Journal of Science and Engineering
- Vol: 12 Issue: 2
- Two-dimensional Chebyshev Polynomials for Solving Two-dimensional Integro-Differential Equations
Two-dimensional Chebyshev Polynomials for Solving Two-dimensional Integro-Differential Equations
Authors : Azim Rivaz, Samane Jahan Ara, Farzaneh Yousefi
Pages : 0-0
View : 7 | Download : 5
Publication Date : 2015-11-01
Article Type : Research
Abstract :In this paper, we present a new approach to obtain the numerical solution of the linear twodimensional Fredholm and Volterra integro-differential equations (2D-FIDE and 2D-VIDE). First, we introduce the two-dimensional Chebyshev polynomials and construct their operational matrices of integration. Then, both of them, two-dimensional Chebyshev polynomials and their operational matrix of integration, are used to represent the matrix form of 2D-FIDE and 2D-VIDE. The main characteristic of this approach is that it reduces 2D-FIDE and 2D-VIDE to a system of linear algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the presented techniqueKeywords : Two-dimensional Fredholm and Volterra integro-differential equations, Two-dimensional Chebyshev polynomials, Operational matrix of integration