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CONNECTING WAVEFORM RELAXATION CONVERGENCE PROPERTIES TO THE A‐ STABILITY OF MULTIRATE INTEGRATION METHODS

J. White (Research Laboratory of Electronics Dept. of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge, MA)
F. Odeh (I.B.M. T. J. Watson Research Center Yorktown Heights, N. Y.)

Abstract

Application of the waveform relaxation algorithm to the differential‐algebraic equations generated by problems in circuit and semiconductor device simulation have demonstrated that the method often contracts uniformly in time. In addition, instabilities in the underlying multirate integration method have not been observed. In this paper, it is proved that multirate A‐stability and waveform relaxation uniform contractivity are connected, and use the result to show that the first and second‐order backward‐difference based multirate methods are A‐stable when applied to block diagonally‐dominant problems.

Citation

White, J. and Odeh, F. (1991), "CONNECTING WAVEFORM RELAXATION CONVERGENCE PROPERTIES TO THE A‐ STABILITY OF MULTIRATE INTEGRATION METHODS", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 10 No. 4, pp. 497-508. https://doi.org/10.1108/eb051724

Publisher

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MCB UP Ltd

Copyright © 1991, MCB UP Limited