PDESYS: INTERACTIVE GRAPHICAL SOFTWARE FOR PARTIAL DIFFERENTIAL EQUATIONS ON MICROCOMPUTERS

THE ULTIMATE GOAL OF THIS RESEARCH IS TO PRODUCE PDESYS, A SOFTWARE PACKAGE FOR PERSONAL COMPUTERS THAT PROVIDES AN INTERACTIVE GRAPHICAL ENVIRONMENT FOR DEFINING, SOLVING, ANDVIEWING THE SOLUTIONS TO SYSTEMS OF PARABOLIC AND ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS (PDE'S) ON ARBITRARY ONE- ANDTWO-DIMENSIONAL SPATIAL DOMAINS. PDE'S OF THE TYPES TO BE HANDLED BY THE PDESYS SOFTWARE ARE UBIQUITOUS IN BIOMEDICINE, SCIENCE, AND ENGINEERING. HEAT TRANSFER, ELECTRODIFFUSION, REACTION DIFFUSION, NERVE-IMPULSE TRANSMISSION, CAPILLARY/TISSUE EXCHANGE, AND MACROMOLECULAR PERCOLATION IN TISSUE ARE ONLY A FEW OF THE MANY AREAS IN WHICH THESE EQUATIONS ARISE. EXISTING PACKAGES FOR SOLVING PDE'S ARE LARGE AND DIFFICULT TO USE, AND NONE OF THEM IS AVAILABLE FOR MICROCOMPUTERS. THESE PACKAGES ARE EFFICIENT ONLY ON SPECIAL PROBLEMS AND PROVIDE UNFRIENDLY USER INTERFACES. THIS RESEARCH WILL DESIGN A SYSTEM THAT WILL BE CONVENIENT, FLEXIBLE, AND EFFICIENT. IT WILL BE SUITABLE FOR USERS WHO ARE LESS TECHNICALLY PROFICIENT IN NUMERICAL ANALYSIS. WHATWILL DISTINGUISH THIS PACKAGE FROM OTHERS IS THAT, WHEN THERE IS A TRADEOFF BETWEEN CONVENIENCE AND EFFICIENCY, IT WILL TILT TOWARD CONVENIENCE. PDESYS WILL USE THE MLAB MODELING LANGUAGE AS ITS INTERACTIVE GRAPHICAL SHELL.