Simultaneous Numerical Solution of Differential-Algebraic Equations

Journal Article · Fri Jan 01 04:00:00 EST 1971 · IEEE Transactions on Circuit Theory

DOI:https://doi.org/10.1109/tct.1971.1083221· OSTI ID:1444803

Gear, C.

This paper discusses a unified method for handling the mixed differential and algebraic equations of the type that commonly occur in the transient analysis of large networks or in continuous system simulation is discussed. The first part of the paper is a brief review of existing techniques of handling initial value problems for stiff ordinary differential equations written in the standard form y' f(y, t) . In the second part one of these techniques is applied to the problem F(y, y', t)=0 . This may be either a differential or an algebraic equation as \partial F/ \partial y' is nonzero or zero. It will represent a mixed system when vectors F and y represent components of a system. The method lends itself to the use of sparse matrix techniques when the problem is sparse.

• Research Organization: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• DOE Contract Number: AC02-76SF00515
• OSTI ID: 1444803
• Report Number(s): SLAC-PUB-0723
• Journal Information: IEEE Transactions on Circuit Theory, Journal Name: IEEE Transactions on Circuit Theory Journal Issue: 1 Vol. 18; ISSN 0018-9324
• Country of Publication: United States
• Language: English