NDLI: <formula formulatype=inline><tex Notation=TeX>$A$</tex></formula>-Stable and <formula formulatype=inline><tex Notation=TeX>$L$</tex></formula>-Stable High-Order Integration Methods for Solving Stiff Differential Equations

Content Provider	IEEE Xplore Digital Library
Author	Gad, E. Nakhla, M. Achar, R. Yinghong Zhou
Copyright Year	1982
Abstract	This paper describes a new A- and L-stable integration method for simulating the time-domain transient response of nonlinear circuits. The proposed method, which is based on the Obreshkov formula, can be made of arbitrary high order while maintaining the A-stability property. The new method allows for the adoption of higher order integration methods for the transient analysis of electronic circuits while enabling them to take larger step sizes without violating the stability, leading to faster simulations. The method can be run in an L-stable mode to handle circuits with extremely stiff equations. Necessary theoretical foundations, implementation details, error-control mechanisms, and computational results are presented.
Sponsorship	IEEE Council on Electronic Design Automation IEEE Circuits and Systems Society
Starting Page	1359
Ending Page	1372
Page Count	14
File Size	1072539
File Format	PDF
ISSN	02780070
Volume Number	28
Issue Number	9
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-09-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Circuit simulation Time domain analysis Transient response Nonlinear circuits Transient analysis Electronic circuits Circuit stability Stability analysis Computational modeling Analytical models stiff circuits $A$-stability circuit simulation high-order integration methods $L$ -stability multiderivative methods numerical solution of differential equations (DEs)
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Electrical and Electronic Engineering Software

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