On the numerical solution of the diffusion equation with variable space operator

In present paper numerical schemes are developed for obtaining approximate solutions to the mixed problem for one-dimensional diffusion equation with variable space operator.The method of lines semidiscretization approach is used to transform the model partial differential equation into a system of first-order linear ordinary differential equations. The partial derivative with respect to the space variable is approximated by the first and second-order finite-difference approximation. For the solution of the resulting system of first-order ordinary differential equations we apply the first and second order of accuracy difference schemes. Stability estimates for the solution of these difference schemes are established. Numerical techniques are developed by applying a procedure of the solution of first order linear difference equation with matrix coefficients. The algorithms are tested on a model problem in biofluid mechanics. Two regions are considered close to the endothelial cells (EC) which can be modeled taking the mixed problem for one-dimensional diffusion equation with variable space operator.