Results 261 to 270 of about 7,385 (298)

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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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.
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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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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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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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Variable-Order ESIRK Methods for Stiff Differential Equations

Numerical Algorithms, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the integration of stiff differential equations

1977
Let us try to integrate the differential equation of Van der Pol y″−e(1−y2)y′+y = 0 with e=100 by a standard integration routine, say, Fehlbergs method of order 7 with step size control.
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Numerical Integration of Systems of Stiff Nonlinear Differential Equations

Bell System Technical Journal, 1968
In connection with the design of transistor circuits, for example, it is frequently necessary to obtain a numerical solution of a system of nonlinear ordinary differential equations. In some cases, these equations possess a property that leads to intolerable computational requirements relative to the use of standard predictor-corrector techniques or ...
Sandberg, I. W., Shichman, H.
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