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Rationalized Haar functions are developed to approximate the solution of the nonlinear Volterra–Fredholm–Hammerstein integral equations. The properties of rationalized Haar functions are first presented. These properties together with the Newton–Cotes nodes and Newton–Cotes integration method are then utilized to reduce the solution of… (More)

- Y. Ordokhani
- 2009

In this paper a numerical method for finding the solution of Fredholm-Hammerstein integral equations is proposed. At first the properties of the Walsh-hybrid functions, which combination of block-pulse functions and Walsh functions are proposed. The properties of the hybrid functions with the operational matrix of integration together Newton-Cotes nodes are… (More)

- Y. Ordokhani
- 2008

A numerical method for finding the solution of nonlinear Volterra-Hammerstein integral equations is proposed. The properties of the hybrid functions which consists of block-pulse functions plus rationalized Haar functions are presented. The hybrid functions together with the operational matrices of integration and product are then utilized to reduce the… (More)

A numerical technique for solving the classical brachistochrone problem in the calculus of variations is presented. The brachistochrone problem is first formulated as a nonlin-ear optimal control problem. Application of this method results in the transformation of differential and integral expressions into some algebraic equations to which Newton-type… (More)

This paper presents an appropriate numerical method to solve nonlinear Fredholm integro-differential equations with time delay. Its approach is based on the Taylor expansion. This method converts the integro-differential equation and the given conditions into the matrix equation which corresponds to a system of nonlinear algebraic equations with unknown… (More)