Two Methods of Solving Heat and Wave Problems
DOI:
https://doi.org/10.5540/tema.2008.09.01.0063Abstract
Two methods of solving a large class of heat and wave problems are described. The problems are two-dimensional and exhibit not only non-homogeneity of the differential equation and of the initial and boundary conditions but also time dependence of the sources and of the initial and boundary data. The two corresponding solutions are proved to be equal, and an illustration of the methods is provided by applying them to solve a specific problem using the polar coordinates.References
[1] E. Butkov, “Mathematical Physics”, Addison-Wesley Publishing Company, Reading, Massachusetts, 1973.
F.B. Hildebrand, “Advanced Calculus for Applications”, Second Edition, Prentice-Hall, Englewood Cliffs, New Jersey, 1976.
J.D. Jackson, “Classical Electrodynamics”, John Wiley & Sons, Second Edition, New York, 1975.
F. John, “Partial Differential Equations”, Third Edition, Springer-Verlag, New York, 1978.
K.R. Symon, “Mechanics”, Third Edition, Addison-Wesley Publishing Company, Reading, Massachusetts, 1971.
E.C. Zachmanoglou, D.W. Thoe, “Introduction to Partial Differential Equations with Applications”, The Williams & Wilkins Company, Baltimore, 1976.
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