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Robust Numerical Integration Using Wave-Digital Concepts

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Abstract

Numerical integration of linear and nonlinear ordinary and partial differential equations describing physically realistic systems can be achieved by means of principles derived from those originally developed in the context of wave digital filters, thus in a specialized branch of the broader area of digital signal processing. The method draws maximum advantage of essential physical properties of such systems, in particular of causality, passivity, finiteness of propagation velocities etc. and makes use of the trapezoidal rule for approximating the differential operators. This way it has the unique advantage of simultaneously offering second-order accuracy, high robustness and fault tolerance, massive parallelism, full localness (also for taking into account arbitrary boundary conditions and shapes), and explicit or at least semi-explicit computability. A brief overview of the method is given.

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Authors and Affiliations

  1. Ruhr-Universität Bochum, Bochum, Germany

    Alfred Fettweis

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  1. Alfred Fettweis
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Correspondence to Alfred Fettweis.

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Published online: February 2006

This paper is a revised version of the one that has appeared under the same title in the Proceedings of the 5th DSPS Educators Conference, pp. 23–32, Tokyo, Japan, 17–18 September 2003

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Fettweis, A. Robust Numerical Integration Using Wave-Digital Concepts. Multidim Syst Sign Process 17, 7–25 (2006). https://doi.org/10.1007/s11045-005-6236-3

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