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Structural Characterization and Efficient Implementation Techniques for A -Stable High-Order Integration Methods

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4 Author(s)
Yinghong Zhou ; Cadence Design Syst., Inc., San Jose, CA, USA ; Gad, Emad ; Nakhla, M.S. ; Achar, R.

This paper presents structural characterization and performance enhancement strategies for the recently proposed A-stable and L-stable high-order integration methods based on the Obreshkov formula. It is demonstrated that although the Jacobian matrix in these methods has a bigger size than the Jacobian matrix in classical low-order methods, it enjoys a special structure that can be used to develop efficient factorization techniques. In addition, the paper proposes a method to reduce the number of Newton-Raphson iterations needed to converge in the large Jacobian domain.

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Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on  (Volume:31 ,  Issue: 1 )