Solution of nonlinear singular initial value problems of generalized Lane-Emden type using block pulse functions in a large interval

In this paper, the block pulse functions (BPFs) and their operational matrices of integration and differentiation are used to solve nonlinear singular initial value problems (NSIVPs) of generalized Lane-Emden type in a large interval. In the proposed method, we present a new technique for computing nonlinear terms in such equations. This technique is then utilized to reduce the solution of this nonlinear singular initial value problems to a system of nonlinear algebraic equation whose solution is the coefficients of block pulse expansions of the solution of NSIVPs. Numerical examples are illustrated to show the reliability and efficiency of the proposed method.