Computer Algebra in Simulation Code Development

Richard Liska

The majority of large-scale scientific computation problems fall into the area of numerical simulations of real world systems. Such systems are usually described by a mathematical model in the form of a system of partial differential equations (PDEs) which are solvable only numerically. The productivity of particular numerical PDEs solver development can be increased by using special program tools. Such tools are usually implemented in a computer algebra system. The FIDE package includes several tools performing such tasks as PDEs discretization, analysis of difference schemes and generation of numerical code for difference schemes solving. Capabihty of using the package for a real hard simulation problem is illustrated. Possibilities to enlarge the abilities of such tools and to incorporate artificial intelligence methods in the presented methodology are discussed.


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