Title: Computer facilitated mathematical techniques of differential equations governing engineering processes

Authors: F.H. Bellamine, H. Fgaier

Addresses: The National Institute of Applied Science and Technology in Tunis, Centre Urbain Nord, B.P.N 676, 1080 Tunis Cedex, Tunisia. ' Department of Mathematics and Statistics, University of Guelph, 50 Stone Road East, Guelph, ON N1G 2W1, Canada

Abstract: Appropriate mathematical methods are very important in solving differential equations modelling engineering and physical processes. The present article introduces the use of symbolic packages as a way to facilitate considerably the search for solutions, and eliminates the drudgery associated with routine algebraic manipulations. A number of examples illustrating various solution techniques such as similarity transformation, eigenfunction expansion, transformation to a class form, and transformation to a suitable coordinate system are provided. These techniques are implemented in Maple, and the provided illustrations show that the complexity of studying engineering processes is significantly reduced. The paper also discusses how attractive and informative graphical displays in animated form can be obtained from the solution.

Keywords: partial differential equations; PDEs; symbolic computation; Maple; applied mathematics; engineering processes; graphics; animation; engineering education.

DOI: 10.1504/WRSTSD.2008.020276

World Review of Science, Technology and Sustainable Development, 2008 Vol.5 No.3/4, pp.234 - 252

Published online: 14 Sep 2008 *

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