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Selective Computation—VI: Stiff Differential equations

Nonlinear Analysis: Theory, Methods & Applications, 1979
IN THIS paper, we wish to consider stiff differential equations. This is a very serious problem computationally and very interesting analytically. It is relevant to selective computation since stiffness is very significant in case we want to do long term integration. In Section 2, we make some comments about the origins of stiffness.
exaly   +2 more sources

Linearizing Stiff Delay Differential Equations [PDF]

Applied Mathematics & Information Sciences, 2013
This paper deals to the study and approximation of stiff delay differential equations based on an analysis of a certain error functional. In seeking to minimize the error by using standard descent schemes, the procedure can never get stuck in local minima, but will always and steadily decrease the error until getting to the solution sought.
S. Amat, M L�egaz, P. Pedregal
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On an L-stable method for stiff differential equations

Information Processing Letters, 1977
exaly   +3 more sources

A reliable rosenbrock integrator for stiff differential equations

Computing, 1981
This note points out that the reliability of step-by-step integrators for ordinary differential equations can be increased considerably by a simple trick. We incorporated this idea into a program based on an A-stable Rosenbrock formula. This program comprises about 100 statements only and gives good numerical results.
Björn A. Gottwald, Gerhard Wanner
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Methods for stiff differential equations

ACM SIGNUM Newsletter, 1973
Under supervision of professor G. Dahlquist different approaches to the numerical solution of stiff differential equations have been studied at our institute. As an introduction to the subject a survey of methods and applications up to 1970 (1) was made.
G. Bjurel, B. Lindberg
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A Method for Solving Certain Stiff Differential Equations

SIAM Journal on Applied Mathematics, 1978
Certain differential equations that arise when solving chemical kinetics problems which have widely differing time constants are analyzed by a method that implicitly separates the fast reacting components from the remaining components of the system.
Clasen, Richard J., Garfinkel, David, Shapiro, Norman Z., Roman, Gruia- Catalin   +3 more
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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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Predicting stiff ordinary differential equations with stiffness coefficient

Australian Journal of Mechanical Engineering, 2014
Stiff ordinary differential equations (ODEs) are present in engineering, mathematics, and sciences. Identifying them for effective simulation is imperative. This paper considers only linear initial value problems and brings to light the fact that stiffness ratio or coefficient of a suspected stiff dynamic system can be elusive as regards the phenomenon
B K Aliyu, C U Nwojiji, A O Kwentoh
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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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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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