a collocation method for solving nonlinear differential equations via hybrid of rationalized haar functions

hybrid of rationalized haar functions are developed to approximate the solution of the differential equations. the properties of hybrid functions which are the combinations of block-pulse functions and rationalized haar functions are first presented. these properties together with the newton-cotes nodes are then utilized to reduce the differential equations to the solution of algebraic equations. the method is computationally attractive, and applications are demonstrated through illustrative examples.