Numerical Solution of Fredholm Integro-differential Equations By Using Hybrid Function Operational Matrix of ‎Differentiation‎

Subject Areas : International Journal of Industrial Mathematics

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.)

Received: 2018-03-19 Accepted : 2018-03-19 Published : 2017-09-01

Keywords: Fredholm integro-differential , Hybrid function, Chebyshev polynomial, Block-pulse function, Operational matrix of &amp, lrm, der,

Abstract :

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.‎