Abstract
As has been shown, attractive methods for numerically integrating partial differential equations (PDEs) resulting from physical problems can be obtained by simulating the actual physical passive (conservation of energy) dynamical system by means of a discrete passive dynamical system, and this in such a way that the full parallelism and the exclusively local nature of the interconnections (principle of action at proximity) are preserved. An alternative approach for developing such methods is presented which, while still using principles of the same type as those on which multidimensional wave digital filters (WDFs) are based, involves appropriate transformations of the original coordinates of the physical problem at hand. This alternative approach is not only easier to apply than the one referred to above but also more general; it is illustrated on the one hand by the same examples as those that have been used for the other approach, and on the other by showing the applicability to Maxwell's equations.
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Fettweis, A., Nitsche, G. Transformation approach to numerically integrating PDEs by means of WDF principles. Multidim Syst Sign Process 2, 127–159 (1991). https://doi.org/10.1007/BF01938221
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DOI: https://doi.org/10.1007/BF01938221