Abstract
In this paper, a method for numerical integration of partial differential equations (PDEs) in safety critical applications is suggested, based on multidimensional wave digital filters (MDWDFs). In comparison to other numerical integration methods the WD method has an outstanding robustness. WDFs have an excellent behavior against stability problems, like the prevention of overflow-errors and negative effects due to rounding errors, even in the case of limited wordlength. It seems that these outstanding properties make this method predestinated for the usage in safety critical applications. In our research project, we want not only to examine the theory but, the WD method is embedded in the commercial instrumentation & control (I&C)-system TELEPERM XS. In order to preserve all safety features, we verify the used C-language implementations by means of formal methods of software engineering.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Fettweis, A.: Entwurf von Digitalfiltern in Anlehnung an Verfahren der klassischen Netzwerktheorie. NTZ-Fachtagung 15./16.10.1970 Stuttgart (1970)
Fettweis, A.: Wave digital filters: Theory and Practice (invited paper). Proceedings of the IEEE (The Institute of Electrical and Electronics Engineers) 74(2), 270–327 (1986); (Correction to “. . . ”, no. 75, vol. 5, p. 729
Fettweis, A.: Multidimensional wave digital filters, Genoa, Italy, vol. 2, pp. 409–416 (1976)
Fischer, H.D.: Wave digital filters for numerical integration. ntz-Archiv, Bd. 6 (2), S.37–S.40 (1984)
Fettweis, A., Nitsche, G.: Massively parallel algorithms for numerical integration of partial differential equations. In: International Workshop on Algorithms and Parallel VLSI Architectures, Summaries of Contributions, Pont-à-Mousson, France, pp. S.475–S.484 (1990)
McCarthy, J.: Towards a Mathematical Science of Computation. In: Proceedings of the IFIP Congress, pp. S.21–S.28. North-Holland, Amsterdam (1962)
Hoare, C.: An Axiomatic Basis for Computer Programming. CACM, Bd. 12 (10), S.576–S.580+583 (1969)
Bose, N.K.: Applied Multidimensional System Theory. Van Nordstrand Reinhold Company (1982)
Meerkötter, K.: Beiträge zur Theorie der Wellendigitalfilter. Doctoral dissertation, Ruhr-Universität Bochum (1979)
Ochs, K.: Passive Integration Methods: Fundamental Theory. Archiv für Elektronik und Übertragungstechnik, Bd. 55(3), S. 153–163 (2001)
Seshu, S., Reed, M.B.: Linear Graphs and Electrical Networks. Addison-Wesley, Reading (1961)
Vollmer, M.: An approach to automatic generation of wave digital structures from pdes. In: Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS 2004), Vancouver, Canada, 23 May - 26 May (2004)
Gödel, K.: Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik 38, 173–198 (1931)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vollmer, M. (2004). Numerical Integration of PDEs for Safety Critical Applications Implemented by I&C Systems. In: Heisel, M., Liggesmeyer, P., Wittmann, S. (eds) Computer Safety, Reliability, and Security. SAFECOMP 2004. Lecture Notes in Computer Science, vol 3219. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30138-7_23
Download citation
DOI: https://doi.org/10.1007/978-3-540-30138-7_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23176-9
Online ISBN: 978-3-540-30138-7
eBook Packages: Springer Book Archive