Acceleration of Runge-Kutta integration schemes.

Phomomsiri, Phailaung; Udwadia, Firdaus E.

Displaying similar documents to “Acceleration of Runge-Kutta integration schemes.”

Central WENO schemes for hyperbolic systems of conservation laws

Doron Levy, Gabriella Puppo, Giovanni Russo (1999)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Accelerated Runge-Kutta methods.

Udwadia, Firdaus E., Farahani, Artin (2008)

Discrete Dynamics in Nature and Society

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Comparison of time stepping schemes on the cable equation.

Li, Chuan, Alexiades, Vasilios (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Zero Dissipative DIRKN Pairs of Order 5(4) for Solving Special Second Order IVPs

S. O. Imoni, M. N. O. Ikhile (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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For initial value problem (IVPs) in ordinary second order differential equations of the special form $y^{''} = f (x, y)$ possessing oscillating solutions, diagonally implicit Runge–Kutta–Nystrom (DIRKN) formula-pairs of orders 5(4) in 5-stages are derived in this paper. The method is zero dissipative, thus it possesses a non-empty interval of periodicity. Some numerical results are presented to show the applicability of the new method compared with existing Runge–Kutta (RK) method applied to the problem...

Explicit two-step Runge-Kutta methods

Zdzisław Jackiewicz, Rosemary Anne Renaut, Marino Zennaro (1995)

Applications of Mathematics

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The explicit two-step Runge-Kutta (TSRK) formulas for the numerical solution of ordinary differential equations are analyzed. The order conditions are derived and the construction of such methods based on some simplifying assumptions is described. Order barriers are also presented. It turns out that for order $p \leq 5$ the minimal number of stages for explicit TSRK method of order $p$ is equal to the minimal number of stages for explicit Runge-Kutta method of order $p - 1$ . Numerical results are presented...

Nine-stage Multi-derivative Runge-Kutta method of order 12

Truong Nguyen-Ba, Vladan Božić, Emmanuel Kengne, Rémi Vaillancourt (2009)

Publications de l'Institut Mathématique

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Stability of discrete shocks for difference approximations to systems of conservation laws.

Nicola, Aurelian (2005)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Full discretization of some reaction diffusion equation with blow up

Geneviève Barro, Benjamin Mampassi, Longin Some, Jean Ntaganda, Ousséni So (2006)

Open Mathematics

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This paper aims at the development of numerical schemes for nonlinear reaction diffusion problems with a convection that blows up in a finite time. A full discretization of this problem that preserves the blow - up property is presented as well as a numerical simulation. Efficiency of the method is derived via a numerical comparison with a classical scheme based on the Runge Kutta scheme.

Highly anisotropic nonlinear temperature balance equation and its numerical solution using asymptotic-preserving schemes of second order in time

Alexei Lozinski, Jacek Narski, Claudia Negulescu (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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This paper deals with the numerical study of a nonlinear, strongly anisotropic heat equation. The use of standard schemes in this situation leads to poor results, due to the high anisotropy. An Asymptotic-Preserving method is introduced in this paper, which is second-order accurate in both, temporal and spacial variables. The discretization in time is done using an L-stable Runge−Kutta scheme. The convergence of the method is shown to be independent of the anisotropy parameter , and...