MICROCOMPUTER SOFTWARE FOR DIFFERENTIAL EQUATIONS

SOFTWARE WILL BE DEVELOPED THAT WILL ALLOW SCIENTISTS TO QUICKLY AND EASILY SOLVE A WIDE ARRAY OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS ON MICROCOMPUTERS CAPABLE OF RUNNING MICROSOFT WINDOWS OR OS/2 AND ON THE APPLE MACINTOSH FAMILY. THIS SOFTWARE WILL PROVIDE USERS WITH EASY ACCESS TO CAPABILITIES FAR BEYOND THOSE AVAILABLE FROM OTHER MICROCOMPUTER DIFFERENTIAL EQUATION SOLVERS. THESE INCLUDE: THE CHOICE OF A VARIETY OF COMPUTATIONAL TECHNIQUES FOR ODE'S (STIFF AND NON-STIFF MULTISTEP PREDICTOR-CORRECTORS, IMPLICIT RUNGE-KUTTA AND BULIRSCH-STOER);AND SOLUTION OF PDE'S BY THE METHOD OF LINES, BY MOVING FINITE ELEMENT METHODS AND BY VARIOUS ADAPTIVE METHODS. THESE METHODS WILL ALLOW THE SOLUTION OF A WIDE CLASS OF PROBLEMS THAT ARISE IN BIOLOGICAL, PHYSICAL AND CHEMICAL SYSTEMS. A PARTICULARLY POWERFUL FEATURE WILL BE THE INTEGRATION OF THE SOFTWARE INTO THE MICROMATH SCIENTIFIC COMPUTING ENVIRONMENT, WHICH WILL ALLOW CAPABILITIES FOR SOLUTION CHEMICAL EQUILIBRIUM, NONLINEAR LEAST SQUARES PARAMETER ESTIMATION AND NUMERICAL INVERSION OF LAPLACE TRANSFORMS TO ALL BE ACCESSED CONCURRENTLY WITH THE ABILITY TO NUMERICALLY SOLVE DIFFERENTIAL EQUATIONS. THIS SOFTWARE WILL BE A POWERFUL AND EASY-TO-USE MODEL DEVELOPMENT TOOL FOR SCIENTISTS, ENGINEERS, UNDERGRADUATES AND GRADUATE STUDENTS IN THE HEALTH SCIENCES. BOTH STUDENTS AND RESEARCHERS WHO USE THIS SOFTWARE WILL BE ABLE TO FOCUS THEIR ATTENTION ON THE CONCEPTUAL ISSUES OF THE PROBLEM UNDER INVESTIGATION, WITHOUT EXPENDING ENERGY ON THE NUMERICAL MATHEMATICAL DETAILS OF GENERATING SOLUTIONS.