Estimating the error of numerical solutions of systems of reaction-diffusion equations

The ever increasing activity in the areas of mathematics and science concer ned with reaction-diffusion equations marks both their important role in mo deling physical phenomena in such diverse fields as biology, chemistry, met allurgy, and combustion, and the beauty and complexity found in their solut ions. Numerical analysis of reaction-diffusion equations has become a centr al tool in their study because of the many barriers that exist for mathemat ical analysis. It is exactly these situations, when we know little about th e true solution, that are particularly needful of accuracy in numerical res ults. Yet, these same analytic difficulties also give rise to nearly insurm ountable barriers to accurate analytic estimation of the error of numerical solutions. In this paper, we investigate a different approach to this prob lem based on the computational estimation of the error of numerical solutio ns.