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

Document Type : Research Paper


Department of Mathematics‎, ‎Karaj Branch‎, ‎Islamic Azad University‎, ‎Karaj‎, ‎Iran‎.


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.‎