Results 241 to 250 of about 120,633 (286)

Contractive methods for stiff differential equations Part II

BIT, 1978
An integration method for ordinary differential equations is said to be contractive if all numerical solutions of the test equationx′=λx generated by that method are not only bounded (as required for stability) but non-increasing. We develop a theory of contractivity for methods applied to stiff and non-stiff, linear and nonlinear problems. This theory
Nevanlinna, Olavi, Liniger, Werner
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Solving stiff Lyapunov differential equations

Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334), 2000
We propose a method based on the matrix generalization of the backward differentiation formula for solving stiff Lyapunov differential equations. This method turns a Lyapunov differential equation into an algebraic Lyapunov equation so that the structure of the original equation can be exploited.
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Methods for Solving Stiff Differential Equations

SIMULATION, 1982
In the conclusion of the paper "Solving Stiff Differen tial Equations in the Simulation of Physical Systems (Simulation, Aug. 1981) T.D. Bui states, "The results ... show that LSTIFF is much more effective and reliable than the well-known GEAR program." This statement could be misleading to readers who are not familiar with stiff integration methods ...
R.E. Crosbie, S. Javey
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Stiffness and Non-Stiff Differential Equation Solvers

1975
The effects of stiffness are investigated for production codes for solving non-stiff ordinary differential equations. First, a practical view of stiffness as related to methods for non-stiff problems is described. Second, the interaction of local error estimators, automatic step size adjustment, and stiffness is studied and shown normally to prevent ...
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Difference Methods for Stiff Ordinary Differential Equations

SIAM Journal on Numerical Analysis, 1978
Consider the initial value problem for a first order system of stiff ordinary differential equations.
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General Linear Methods for Stiff Differential Equations

BIT Numerical Mathematics, 2001
A general class of numerical methods for stiff initial value problems that contains both the linear multistep and Runge-Kutta methods is considered. The aim of the author is to obtain particular methods that combine the low computational cost shared by the standard backward differential formula (BDF) methods of the class of multistep methods with the ...
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Typical problems for stiff differential equations

ACM SIGNUM Newsletter, 1975
The solution of stiff differential equations has become a very active area in recent years. To have some idea as to the wishes of practitioners would be of obvious value to researchers developing new tools, to software designers producing new codes, and to those evaluating the codes available at present.
M. K. Gordon, L. F. Shampine
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STIFF DIFFERENTIAL EQUATIONS

Annual Review of Biophysics and Bioengineering, 1977
D, Garfinkel, C B, Marbach, N Z, Shapiro
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Stiff ordinary differential equation test problems

ACM SIGNUM Newsletter, 1973
Many practical methods for integrating stiff systems of ordinary differential equations are based on underlying theory whose validity is only beyond doubt where the eigenvector system of the Jacobian matrix is constant. Realisation of this fact led the author to develop a range of simple linear test problems, which are described in this note, and which
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Step control criteria for stiff equations

ACM SIGNUM Newsletter, 1974
In a recent note [1], J. C. Butcher showed using a simple 2 stage first order Runge-Kutta method that an error per unit step criterion gave consistent results on a nonstiff problem while an error per step criterion did not. This note considers the effect of employing error per unit step when stiff equations are involved.
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