Numerical solution of a diffusion equation - reaction by the nite difference method

Abstract

This article shows by numerical way the one-dimensional diffusion-reaction problema:

[Equation 1]

Where f and u are elements of certain funtional spaces. The results about existence and unicity as well as 0 determination of blow-up solutions has been demonstrated by semigroup operators methods. To find the numerical solution. To find the numerical solution I used the Finite Difference Method (MDF) with the Explicit Method, that is, we have discretized the second order spatial derivative using centered differences and the temporal derivative using first orden derivatives and forward. The FDM's programming has been developed in two parts: the writing of the code and execution were done in C programming language and, the graphics were visualized in Scilab. Also, the criteria of stability, consistency and convergence have been studied and analyzed, leading to the conclusion that the FDM is conditionally stable, consistent and convergent.