SBIR-STTR Award

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.Awardee's statement of the potential commercial applications of the research:The software developed under this grant will be useful to a broad range of scientific and technical personnel. Individuals in medical, chemical, biological and natural sciences will be able to simply and easily solve the systems of differential equations that arises from the experiments being conducted in their own labs.

Thesaurus Terms:
computer program /software, computer system design /evaluation, mathematical model, microcomputer

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 MS-DOS, the Apple Macintosh and UNIX operating systems. 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 ODEs (stiff and non-stiff solvers), and the solution of PDEs 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. The software will be capable of parameter estimation for both ODEs and PDEs, and will be capable of handling delay equations and difference equations. In the later part of Phase II, the software will be incorporated into the MicroMath Scientific Computing Environment, a modular system for general scientific problem-solving currently being proposed. The Phase II DIFFEQ software will be a powerful and easy-to-use model development tool for scientists, engineers, undergraduates and graduate students in the health sciences.Awardee's statement of the potential commercial applications of the research:The software developed will be useful to a wide range of scientific, academic, engineering and technical personnel. Individuals in medical, chemical, biological and natural science, and various fields in engineering, would be able to quickly and easily solve the systems of differential equations that arise from the experiments conducted in their own laboratories.

Thesaurus Terms:
computer program /software, computer programming, mathematical model, mathematics, method development, model design /development artificial intelligence, chemical kinetics, computer data analysis, computer graphics /printing, computer human interaction, machine language microcomputer National Institute of General Medical Sciences (NIGMS)