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Published in:
2017 | OriginalPaper | Chapter
20. Alternate Methods of Solution for Heat and Wave Equation Problems
Authors : David J. Wollkind, Bonni J. Dichone
Published in: Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences
Publisher: Springer International Publishing
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Abstract
In this chapter, the Laplace transform (first introduced in Chapter 7) method of solution is employed to solve the problems of heat conduction in a laterally insulated semi-infinite or infinite bar that had been solved by a similarity solution method in Chapter 6 and Problem 6.1, respectively. The Laplace transform method of solving the latter problem involves the use of a Dirac delta function which is introduced in a pastoral interlude. Then the sound wave problem, the solution of which had been obtained in Chapter 12 by employing D’Alembert’s characteristic coordinate method, is solved by using a Fourier integral approach.