Abstract
In this chapter, procedures will be developed for classifying partial differential equations as elliptic, parabolic or hyperbolic. The different types of partial differential equations will be examined from both a mathematical and a physical viewpoint to indicate their key features and the flow categories for which they occur.
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References
Ames, W.F. (1969): Numerical Methods for Partial Differential Equations ( Barnes and Noble, New York )
Belotserkovskii, O.M., Chushkin, P.I. (1965): In Basic Developments in Fluid Dynamics, ed. by M. Holt ( Academic, New York ) pp. 1–126
Chester, C.R. (1971): Techniques in Partial Differential Equations, ( McGraw-Hill, New York )
Courant, R., Friedrichs, K.O. (1948): Supersonic Flow and Shock Waves ( Interscience, New York )
Courant, R., Hilbert, D. (1962): Methods of Mathematical Physics, Vol II ( Interscience, New York )
Fletcher, C.A.J. (1983): “The Galerkin Method and Burgers’ Equation”, in Numerical Solution of Differential Equations, ed. by J. Noye (North-Holland, Amsterdam) pp. 355–475
Garabedian, P. (1964): Partial Differential Equations ( Wiley, New York )
Gelfand, I.M., Shilov, G.E. (1967): Generalised Functions, Vol. 3. Theory of Differential Equations ( Academic, New York )
Gustafson, K.E. (1980): Partial Differential Equations and Hilbert Space Methods ( Wiley, New York )
Hellwig, G. (1964): Partial Differential Equations, An Introduction ( Blaisdell, New York )
Jeffrey, A., Taniuti, T. (1964): Nonlinear Wave Propagation with Applications to Physics and Magnetohydrodynamics ( Academic, New York )
Lighthill, M.J. (1958): Fourier Analysis and Generalised Functions ( Cambridge University Press, Cambridge )
Whitham, G. (1974): Linear and Nonlinear Waves ( Wiley, New York )
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© 1988 Springer-Verlag Berlin Heidelberg
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Fletcher, C.A.J. (1988). Partial Differential Equations. In: Computational Techniques for Fluid Dynamics 1. Springer Series in Computational Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97035-1_2
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DOI: https://doi.org/10.1007/978-3-642-97035-1_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-97037-5
Online ISBN: 978-3-642-97035-1
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