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Almost RungeKutta Methods for Stiff and NonStiff Problems
"... Ordinary differential equations arise frequently in the study of the physical world. Unfortunately many cannot be solved exactly. This is why the ability to solve these equations numerically is important. Traditionally mathematicians have used one of two classes of methods for numerically solving o ..."
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methods. This is a special class of general linear methods which retains many of the properties of traditional Runge–Kutta methods, but with some advantages. Most of this thesis concentrates on explicit methods for nonstiff differential equations, paying
RungeKutta Methods for Hyperbolic Conservation Laws with Stiff Relaxation Terms
 J. Comput. Phys
, 1995
"... Underresolved numerical schemes for hyperbolic conservation laws with stiff relaxation terms may generate unphysical spurious numerical results or reduce to lower order if the small relaxation time is not temporally wellresolved. We design a second order RungeKutta type splitting method that posse ..."
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Cited by 65 (15 self)
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Underresolved numerical schemes for hyperbolic conservation laws with stiff relaxation terms may generate unphysical spurious numerical results or reduce to lower order if the small relaxation time is not temporally wellresolved. We design a second order RungeKutta type splitting method
Parallel Linear System Solvers for RungeKutta Methods
, 1997
"... If the nonlinear systems arising in implicit RungeKutta methods like the Radau IIA methods are iterated by (modified) Newton, then we have to solve linear systems whose matrix of coefficients is of the form I  AhJ with A the RungeKutta matrix and J an approximation to the Jacobian of the righthan ..."
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If the nonlinear systems arising in implicit RungeKutta methods like the Radau IIA methods are iterated by (modified) Newton, then we have to solve linear systems whose matrix of coefficients is of the form I  AhJ with A the RungeKutta matrix and J an approximation to the Jacobian
Stiffness Detection and Estimation of Dominant Spectrum with Explicit RungeKutta Methods
, 1997
"... A new stiffness detection scheme based on explicit RungeKutta methods is proposed. It uses a Krylov subspace approximation to estimate the eigenvalues of the Jacobian of the differential system. The numerical examples indicate that this technique is a worth while alternative to other known stiff ..."
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A new stiffness detection scheme based on explicit RungeKutta methods is proposed. It uses a Krylov subspace approximation to estimate the eigenvalues of the Jacobian of the differential system. The numerical examples indicate that this technique is a worth while alternative to other known
SimulationBased Analysis of Parallel RungeKutta Solvers
"... Abstract. We use simulationbased analysis to compare and investigate different sharedmemory implementations of parallel and sequential embedded RungeKutta solvers for systems of ordinary differential equations. The results of the analysis help to provide a better understanding of the locality and ..."
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Abstract. We use simulationbased analysis to compare and investigate different sharedmemory implementations of parallel and sequential embedded RungeKutta solvers for systems of ordinary differential equations. The results of the analysis help to provide a better understanding of the locality
SMRK: A Parallel Implementation of Multistep RungeKutta methods for Stiff ODEs
"... This paper describes the development of a parallel code for solving stiff Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) using iterated Variable step Multistep RungeKutta (VMRK) methods. It is the continuation of the work on the Nonstiff solver [11]. Since some major mo ..."
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This paper describes the development of a parallel code for solving stiff Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) using iterated Variable step Multistep RungeKutta (VMRK) methods. It is the continuation of the work on the Nonstiff solver [11]. Since some major
An implicit Runge–Kutta method for integration of differential algebraic equations of multibody dynamics
 Numer. Alg
, 2003
"... This paper has not been submitted elsewhere in identical or similar form, nor will it be during the first three months after its submission to Multibody System Dynamics. Abstract. When performing dynamic analysis of a constrained mechanical system, a set of index 3 differential algebraic equations ( ..."
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is constructed with the goal of leveraging with minimal effort established off the shelve implicit ODE integrators for efficiently solving the DAE of multibody dynamics. This concept is demonstrated by embedding a wellknown public domain singly diagonal implicit RungeKutta code in the framework provided
Convergence of RungeKutta methods for delay differential equations
, 1999
"... This paper deals with the adaptation of RungeKutta methods to the numerical solution of (nonstiff) initial value problems for delay differential equations. We consider the interpolation procedure proposed by In 't Hout [8], and prove the new and positive result that for any given RungeKutta ..."
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This paper deals with the adaptation of RungeKutta methods to the numerical solution of (nonstiff) initial value problems for delay differential equations. We consider the interpolation procedure proposed by In 't Hout [8], and prove the new and positive result that for any given RungeKutta
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