Computer facilitated mathematical techniques of differential equations governing engineering processes

摘要

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.