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.