Mathematical models for time evolution can be formulated as integral equations, such as Fredholm and Volterra equations. Such models are of increasing importance in some areas of physics, mechanics and mathematical biology. However, numerical methods for simulation of such models are not well developed yet. In this work, numerical solution of Fredholm and Volterra integral equations of the second kind with constant delay via combined Block-Pulse functions and Legendre polynomials are proposed. The properties of these hybrid functions are presented and then by use of expanding the various time unknown function as their truncated hybrid functions and some matrix properties such as operational matrix of integration, product and delay matrices besides the collocation method we convert these delay integral equations into algebraic equations that can be solved by known method. Some numerical examples are provided to illustrate the accuracy and computational eciency of the method.

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