Mathematical modeling of diffusion problem

This work aims to introduce a numerical approximation procedure based on an operational matrix of block pulse functions, which is employed in solving integral-algebraic equations arising from the 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 an operational matrix to 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.