Abstract
The boundary value problems of the previous chapter are distinguished by the fact that it is possible to derive more or less explicit solutions for the cases considered. A partial exception to this is the problem of the wave equation with an elastic constraint, for which the solution breaks the standard Fourier series mold.
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References
A. K. Aziz, editor, Symposium on the Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, University of Maryland, Baltimore. Academic Press, New York, New York, 1972.
R. E. Banks, PLTMG: A software Package for Solving Elliptic Partial Differential Equations. Society for Industrial and Applied Mathematics, Philadelphis, Pennsylvania, 1990.
C. M. Bender and S. A. Orzag, Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill, New York, New York, 1978.
D. H. Norrie and C. de Vries, An Introduction to Finite Element Analysis. Academic Press, New York, New York, 1978.
E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations. McGraw-Hill, New York, New York, 1955.
E. T. Whittaker and C. N. Watson, A Course of Modern Analysis. Cambridge University Press, Cambridge, England, 4th edition, 1927.
K. E. Gustafson, Introduction to Partial Differential Equations and Hilbert Space Methods. John Wiley and Sons, New York, New York, 1980.
Mathworks Incorporated. Partial Differential Equation Toolbox User’s Guide. Mathworks Incorporated, Natick, Massachusetts, 2000.
J. E. Marsden and A. J. Tromba, Vector Calculus. W. H. Freeman, San Francisco, California, 1976.
C. C. Lin and L. A. Segel, Mathematics Applied to Deterministic Problems in the Natural Sciences. MacMillan, New York, New York, 1974.
W. Miller, Lie Theory and Special Functions. Academic Press, New York, New York, 1968.
L. M. Milne-Thompson, Theoretical Hydrodynamics. MacMillan, London, England, 4th edition, 1962.
P. M. Morse and H. Feshbach, Methods of Theoretical Physics. McGraw-Hill, New York, New York, 1953.
R. Courant and D. Hilbert, Methods of Mathematical Physics, volume 1. Interscience, New York, New York, 1953.
R. Courant and D. Hilbert, Methods of Mathematical Physics, volume 2. Interscience, New York, New York, 1962.
C. D. Smith, Numerical Solution of Partial Differential Equations. Oxford University Press, London, England, 1965.
C. D. Smith, Numerical Solution of Partial Differential Equations. Oxford University Press, London, England, 1965.
J. A. Sommerfeld, Mechanics of Deformable Bodies. Academic Press, New York, New York, 1964.
J. A. Sommerfeld, Partial Differential Equations in Physics. Academic Press, New York, New York, 1964.
W. C. Strang and C. J. Fix, An Analysis of the Finite Element Method. Prentice-Hall, Englewood Cliffs, New Jersey, 1973.
E. C. Titchmarsh, Eigenfunction Expansions Associated With Second Order Differential Equations. Oxford University Press, London, England, 1946.
C. N. Watson, A Treatise on the Theory of Bessel Functions. Cambridge University Press, Cambridge, England, 2nd edition, 1944.
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Davis, J.H. (2004). Sturm-Liouville Theory and Boundary Value Problems. In: Methods of Applied Mathematics with a MATLAB Overview. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8198-2_4
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DOI: https://doi.org/10.1007/978-0-8176-8198-2_4
Publisher Name: Birkhäuser, Boston, MA
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