Diagonally-implicit multi-stage integration methods
Applied Numerical Mathematics
Parallel and sequential methods for ordinary differential equations
Parallel and sequential methods for ordinary differential equations
A nonlinear optimization approach to the construction of general linear methods of high order
Journal of Computational and Applied Mathematics
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Numerical Initial Value Problems in Ordinary Differential Equations
Numerical Initial Value Problems in Ordinary Differential Equations
Computer Methods for Circuit Analysis and Design
Computer Methods for Circuit Analysis and Design
A multi-port current source model for multiple-input switching effects in CMOS library cells
Proceedings of the 43rd annual Design Automation Conference
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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.