Numerical Solution of Fredholm Integro-differential Equations By Using Hybrid Function Operational Matrix of Differentiation
الموضوعات : مجله بین المللی ریاضیات صنعتی
R. Jafri
1
(
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
)
R. Ezzati
2
(
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
)
K. ‎Maleknejad‎
3
(
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
)
الکلمات المفتاحية: Fredholm integro-differential , Hybrid function, Chebyshev polynomial, Block-pulse function, Operational matrix of &, lrm, der,
ملخص المقالة :
In this paper, first, a numerical method is presented for solving a class of linear Fredholm integro-differential equation. The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and Block-pulse functions. The application of the proposed operational matrix with tau method is then utilized to transform the integro-differential equations to the algebraic equations. Finally, show the efficiency of the proposed method is indicated by some numerical examples.