Summary
For nonlinear hyperbolic PDEs, the usual spatial discretizations are considered. On an intermediate level of the approximation, there then are systems of nonlinear ODEs with time t the independent variable. Discretizations of t generate the systems of nonlinear equations whose solutions are to be approximated. Consequently, any one of these practical PDE-methods is affected by the following problem areas for discretizations of ODEs: the existence of spurious difference solutions or diverting difference approximations. This is discussed for (a) the Lorenz-equations as derived by means of a Fourier-method from the PDEs of Fluid Dynamics and (b) an application of a longitudinal method of lines in the case of the Burgers PDE.
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© 1993 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
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Adams, E. (1993). On Spurious Difference Solutions of Discretizations of Nonlinear Hyperbolic Differential Equations. In: Donato, A., Oliveri, F. (eds) Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects. Notes on Numerical Fluid Mechanics (NNFM), vol 43. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-87871-7_1
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