mathematical modeling of diffusion problem

This work aims to introduce a numerical approximation procedure based on operational matrix of block pulse functions, which is employed in solving integral-algebraic equations arising from diffusion model. it is known that the integral-algebraic equations belong to the class of singular problems. the main advantage of this method is the reduction of these singular systems by using operational matrix to a linear lower triangular systems of algebraic equations, which is non-singular. an estimation of the error and illustrative instances are discussed to evaluate the validity and applicability of the presented method.