Spreadsheets, PC's and the finite-difference solutions for ecological distribution

Abstract

Abstract High-speed computation with parallel processing is within the grasp of mathematical ecologists and environmental managers. One can imagine the numerical solution of the large set of simultaneous partial differential equations of population dynamics. This would allow for ecosystem model verification and, eventually, for ecosystem management. It is important to differentiate between numerical analysis and programming. Programming is the final stage during which the most efficient possible management tool is produced. Programming will always be best left professional programmers who specialize in an understanding of the idiosyncracies of particular hardware and particular compilers. A necessary preliminary study, a numerical analysis, will always be required to study the numerical difficulties of, say, the finite difference method. Numerical analysis cannot be conducted without a firm understanding of the phenomena and, therefore, will fall within the purview of the numerical ecologist. Numerical analysis is best conducted on simplified versions of the model in order to discern and control the myriad of error types: numerical instability, numerical dispersal, aliasing, etc. In this paper we demonstrate the use of spreadsheets on PC's as an ideal environment for these preliminary studies.