Two-dimensional Chebyshev Polynomials for Solving Two-dimensional Integro-Differential Equations
Two-dimensional Chebyshev Polynomials for Solving Two-dimensional Integro-Differential Equations
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 technique
Keywords:
Two-dimensional Fredholm and Volterra integro-differential equations, Two-dimensional Chebyshev polynomials, Operational matrix of integration,
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- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2009
- Yayıncı: Çankaya Üniversitesi
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