Journal ArticleDOI
Efficient integration methods for stiff systems of ordinary differential equations
TLDR
In this article, linear one-step methods of a novel design are given for the numerical solution of stiff systems of ordinary differential equations, which permit fast integration with increments h of the independent variable adjusted to the slowly varying, dominant solutions.Abstract:
Linear one step methods of a novel design are given for the numerical solution of stiff systems of ordinary differential equations. These methods permit fast integration with increments h of the independent variable adjusted to the slowly varying, dominant solutions. The integration formulas owe their efficiency to combining a reasonable order of accuracy for $h \to 0$ with a precise simulation of specific rapidly varying solutions, and with A-stability in the sense of Dahlquist.read more
Citations
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Journal ArticleDOI
Steady-state analysis of nonlinear circuits with periodic inputs
T.J. Aprille,T.N. Trick +1 more
TL;DR: A Newton algorithm is defined which converges to the steady-state response rapidly and is applied to several nonlinear circuits, showing a considerable reduction in the amount of time necessary to compute the steady -state response.
Journal ArticleDOI
Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique
TL;DR: In this paper, a general fourth order differencing scheme was developed and applied to three viscous test problems to verify the accuracy and applicability of the technique, which is atypical since only three nodes are necessary to obtain the desired fourth order accuracy.
Journal ArticleDOI
A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations
G. D. Byrne,Alan C. Hindmarsh +1 more
TL;DR: Two variable-order, varlable-step size methods for the numerical solution of the initial value problem for ordinary differential equations are presented and some numerical results are given.
Journal ArticleDOI
Stiff differential equations solved by Radau methods
Ernst Hairer,Gerhard Wanner +1 more
TL;DR: In this article, a new implementation of the Radau IIA method with a variable order strategy is described. But the authors do not discuss the theoretical properties of the new algorithm.
Journal ArticleDOI
A survey of sparse matrix research
TL;DR: This paper surveys the state of the art in sparse matrix research in January 1976, and discusses the solution of sparse simultaneous linear equations, including the storage of such matrices and the effect of paging on sparse matrix algorithms.
References
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Book
Matrix iterative analysis
TL;DR: In this article, the authors propose Matrix Methods for Parabolic Partial Differential Equations (PPDE) and estimate of Acceleration Parameters, and derive the solution of Elliptic Difference Equations.