Hybrid of Rationalized Haar Functions Method for Mixed Hammerstein Integral Equations

A numerical method for solving nonlinear mixed Hammerstein integral equations is presented in this paper. The method is based upon hybrid of rationalized Haar functions approximations. The properties of hybrid functions which are the combinations of block-pulse functions and rationalized Haar functions are first presented. The Newton-Cotes nodes and Newton-Cotes integration method are then utilized to reduce the nonlinear mixed Hammerstein integral equations to the solutions algebraic equations. The method is computationally attractive, and applications are demonstrated through illustrative examples.