Mathematical Metaphors: Problem Reformulation and Analysis Strategies - Softcover

Thompson, David E

Softcover

ISBN 10: 1287249140 ISBN 13: 9781287249146

Publisher: Bibliogov, 2013

Synopsis

This paper addresses the critical need for the development of intelligent or assisting software tools for the scientist who is working in the initial problem formulation and mathematical model representation stage of research. In particular, examples of that representation in fluid dynamics and instability theory are discussed. The creation of a mathematical model that is ready for application of certain solution strategies requires extensive symbolic manipulation of the original mathematical model. These manipulations can be as simple as term reordering or as complicated as discovery of various symmetry groups embodied in the equations, whereby Backlund-type transformations create new determining equations and integrability conditions or create differential Grobner bases that are then solved in place of the original nonlinear PDEs. Several examples are presented of the kinds of problem formulations and transforms that can be frequently encountered in model representation for fluids problems. The capability of intelligently automating these types of transforms, available prior to actual mathematical solution, is advocated. Physical meaning and assumption-understanding can then be propagated through the mathematical transformations, allowing for explicit strategy development.

Edition details

• Publisher: Bibliogov
• Publication date: 2013
• Language: English
• ISBN 10: 1287249140
• ISBN 13: 9781287249146
• Binding: Paperback
• Number of pages: 34