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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Displaying similar documents to “Algorithm for construction of explicit -order Runge-Kutta formulas for the systems of differential equations of the 1st order”
Fifth-order Runge-Kutta with higher order derivative approximations.
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.
On the unique solvability of the Runge-Kutta equations.
J.F.B.M. Kraaijevanger, J. Schneid (1991)
Numerische Mathematik
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On the Order Conditions of Runge-Kutta Methods with Higher Derivatives.
E. Gekeler, R. Widman (1986/87)
Numerische Mathematik
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Partitioned Adaptive Runge-Kutta Methods for the Solution of Nonstiff and Stiff Systems.
K. Strehmel, R. Weiner, J. Bruder (1987/88)
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.
Natural Runge-Kutta and Projection Methods.
Marino Zennaro (1988)
Numerische Mathematik
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