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Browse All Reviews > Mathematics Of Computing (G) > Numerical Analysis (G.1) > Ordinary Differential Equations (G.1.7) > Stiff Equations (G.1.7...)
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1-10 of 11
Reviews about "Stiff Equations (G.1.7...)":
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The equilibrium state method for hyperbolic conservation laws with stiff reaction terms
Zhang B., Liu H., Chen F., Wang J. Journal of Computational Physics 263151-176, 2014. Type: Article
Zhang et al. propose a new fractional-step method for the numerical solution of advection equations with stiff source terms. In general, it is too difficult to obtain satisfactory numerical approximate solutions for stiff reaction prob...
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Oct 29 2014 |
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 An efficient family of strongly A-stable Runge-Kutta collocation methods for stiff systems and DAEs: Part II: convergence results
GonzáLez-Pinto S., HernáNdez-Abreu D., Montijano J. Applied Numerical Mathematics 62(10): 1349-1360, 2012. Type: Article
Fully implicit Runge-Kutta methods play an especially important role in the solution of stiff and non-stiff differential equation systems and differential algebraic equations. This paper deals with a new class of s s...
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Feb 4 2013 |
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The behaviour of the local error in splitting methods applied to stiff problems
Kozlov R., Kværnø A., Owren B. Journal of Computational Physics 195(2): 576-593, 2004. Type: Article
The authors of this paper consider the numerical solution, by splitting, of initial value problems for a system of ordinary differential equations. Specifically, they consider equations that can be split into a part that is singularly ...
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Jun 25 2004 |
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Some numerical methods for stiff problems
Butcher J. Computational methods in sciences and engineering (Proceedings of the international conference, Kastoria, Greece, Sep 12-16, 2003) 93-97, 2003. Type: Proceedings
Butcher begins this paper by explaining the concept of stiffness, and its implications for numerical methods. He observes that implicit Runge-Kutta methods have excellent stability, and explains some of the practical issues of evaluati...
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Mar 29 2004 |
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DESI methods for stiff initial-value problems
Butcher J., Cash J., Diamantakis M. ACM Transactions on Mathematical Software 22(4): 401-422, 1996. Type: Article
The authors describe a class of recently developed Runge-Kutta methods. These techniques are known as DESI (diagonally extended singly implicit) methods and have been introduced to overcome limitations of the more standard singly impli...
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Aug 1 1997 |
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Singly-implicit Runge-Kutta methods for retarded and ordinary differential equations
Claus H. Computing 43(3): 209-222, 1990. Type: Article
Building on foundations laid by Bellman (1961), Stetter (1965), Barwell (1975), Butcher, Burrage, and Chipman (1979), and many others, this paper was motivated by stability investigations of wide classes of interpolation and integratio...
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Apr 1 1992 |
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Runge-Kutta interpolants based on values from two successive integration steps
Tsitouras C., Papageorgiou G. Computing 43(3): 255-266, 1990. Type: Article
For some initial value problems in ordinary differential equations, it is important for a numerical method to be capable of efficiently providing accurate continuous approximations in a given step. The authors extend previous work by o...
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Apr 1 1991 |
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Order, stepsize and stiffness switching
Butcher J. Computing 44(3): 209-220, 1990. Type: Article
In a modern program for solving systems of ordinary differential equations, one attempts to incorporate algorithms for changing the stepsize and the integration formula. Many studies have been devoted to the strategies that can be used...
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Apr 1 1991 |
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Asymptotic error expansions for stiff equations: applications
Auzinger W., Frank G., Kirlinger G. Computing 43(3): 223-253, 1990. Type: Article
In preceding papers, the authors determined the asymptotic behavior of the global discretization error of the implicit Euler, midpoint (IMR), and trapezoidal (ITR) rules applied to a class of nonlinear stiff problem...
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Mar 1 1991 |
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On Stetter`s global error estimation in the smooth phase of stiff differential equations
Scholz S. Computing 36(1-2): 43-55, 1986. Type: Article
This paper studies two-stage ROW methods (which are Runge-Kutta type techniques) for integrating initial value Ordinary Differential Equations (ODEs). In particular, the error estimate is studied for the smooth phase of integrating a s...
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Mar 1 1987 |
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