Results 191 to 200 of about 2,297,727 (227)

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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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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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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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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On The Solution of Stiff Ordinary Differential Equations

AIP Conference Proceedings, 2008
In this paper, we considered new method based on simplex integrals for stiff ordinary differential equations. In contrast to Kuntzmann‐Butcher method, this method requires the solution of less simultaneous implicit equations. And numerical examples illustrate the efficiency of this technique.
Y. Zhou, S. Xiang, Michail D. Todorov
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Stiff Systems of Ordinary Differential Equations

2003
The experience of numerical integration of Cauchy problems for ordinary differential equations shows that it is especially the stiff systems that require a special numerical methods. In this chapter the effect of λ-transformations on such systems of ordinary differential equations and on methods of their integration will be considered.
V. I. Shalashilin, E. B. Kuznetsov
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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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Explicit methods in solving stiff ordinary differential equations

International Journal of Computer Mathematics, 2004
In this article, we extended the existing explicit Taylor method and modified it to gain a new explicit Taylor-liked method in solving stiff differential equations. We also considered the stability property for this method since the stability property of the classical explicit fourth order Runge–Kutta (RK4) method is not adequate for the solution of ...
Ahmad, R. R., Yaacob, Nazeeruddin, Mohamed Murid, Ali Hassan   +2 more
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One-Leg Formulas for Stiff Ordinary Differential Equations

SIAM Journal on Scientific and Statistical Computing, 1984
Some one-leg formulae for stiff ordinary differential equations, that are a generalization of the backward differentiation formulae, are obtained. Applied to the standard scalar test problem, \(y'=\lambda y\), with step length h, these new formulae give large regions of instability in the right half-plane \(Re(h\lambda)>0\).
Watanabe, Daniel S., Sheikh, Qasim M.
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