Boundary value methods: The third way between linear multistep and Runge-Kutta methods
نویسندگان
چکیده
منابع مشابه
Stability and B-convergence properties of multistep Runge-Kutta methods
This paper continues earlier work by the same author concerning the stability and B-convergence properties of multistep Runge-Kutta methods for the numerical solution of nonlinear stiff initial-value problems in a Hilbert space. A series of sufficient conditions and necessary conditions for a multistep Runge-Kutta method to be algebraically stable, diagonally stable, Bor optimally B-convergent ...
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A new strategy to avoid the order reduction of Runge-Kutta methods when integrating linear, autonomous, nonhomogeneous initial boundary value problems is presented. The solution is decomposed into two parts. One of them can be computed directly in terms of the data and the other satisfies an initial value problem without any order reduction. A numerical illustration is given. This idea applies ...
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Abstract— General linear methods (GLM) apply to a large family of numerical methods for ordinary differential equations, with RungeKutta (RK) and Almost Runge-Kutta (ARK) methods as two out of a number of special cases. In this paper, we have investigated the efficacy of Richardson extrapolation (RE) technique as a means of obtaining viable and acceptable estimates of the local truncation error...
متن کاملRunge - Kutta Methods page RK 1 Runge - Kutta Methods
Literature For a great deal of information on Runge-Kutta methods consult J.C. Butcher, Numerical Methods for Ordinary Differential Equations, second edition, Wiley and Sons, 2008, ISBN 9780470723357. That book also has a good introduction to linear multistep methods. In these notes we refer to this books simply as Butcher. The notes were written independently of the book which accounts for som...
متن کاملLinear Stability of Partitioned Runge-Kutta Methods
We study the linear stability of partitioned Runge–Kutta (PRK) methods applied to linear separable Hamiltonian ODEs and to the semidiscretization of certain Hamiltonian PDEs. We extend the] by presenting simplified expressions of the trace of the stability matrix, tr Ms, for the Lobatto IIIA–IIIB family of symplectic PRK methods. By making the connection to Padé approximants and continued fract...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1998
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(98)80028-x