Some fundamental tools

Abstract

Mathematical modeling of real-life problems in engineering, physics or life sciences often gives rise to partial differential problems that cannot be solved analytically but need a numerical scheme to obtain a suitable approximation. Dealing with numerical modeling requires first of all an understanding of the underlying differential problem. The type of differential problem, as well as issues of well-posedness and regularity of the solution may indeed drive the selection of the appropriate simulation tool. A second requirement is the analysis of numerical schemes, in particular their stability and convergence characteristics. Last, but not least, numerical schemes must be implemented in a computer language, and often aspects which look easy “on paper” arise complex implementation issues, particularly when computational efficiency is at stake.