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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Displaying similar documents to “Zero Dissipative DIRKN Pairs of Order 5(4) for Solving Special Second Order IVPs”
Nine-stage Multi-derivative Runge-Kutta method of order 12
Fifth-order Runge-Kutta with higher order derivative approximations.
Goeken, David, Johnson, Olin (1999)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Order conditions for partitioned Runge-Kutta methods
Zdzisław Jackiewicz, Rossana Vermiglio (2000)
Applications of Mathematics
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We illustrate the use of the recent approach by P. Albrecht to the derivation of order conditions for partitioned Runge-Kutta methods for ordinary differential equations.
Partitioned Adaptive Runge-Kutta Methods and Their Stability.
K. Strehmel, R. Weiner (1984)
Numerische Mathematik
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Self-similar solutions for the two-dimensional Nernst-Planck-Debye system
Łukasz Paszkowski (2012)
Applicationes Mathematicae
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We investigate the two-component Nernst-Planck-Debye system by a numerical study of self-similar solutions using the Runge-Kutta method of order four and comparing the results obtained with the solutions of a one-component system. Properties of the solutions indicated by numerical simulations are proved and an existence result is established based on comparison arguments for singular ordinary differential equations.
Partitioned Runge-Kutta Methods with Stiffness Detection and Stepsize Control.
Peter Rentrop (1985)
Numerische Mathematik
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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 the minimal number of stages for explicit TSRK method of order is equal to the minimal number of stages for explicit Runge-Kutta method of order . Numerical results are presented...