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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Displaying similar documents to “Fifth-order Runge-Kutta with higher order derivative approximations.”
Partitioned Adaptive Runge-Kutta Methods for the Solution of Nonstiff and Stiff Systems.
On the unique solvability of the Runge-Kutta equations.
J.F.B.M. Kraaijevanger, J. Schneid (1991)
Numerische Mathematik
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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.
On the Order Conditions of Runge-Kutta Methods with Higher Derivatives.
E. Gekeler, R. Widman (1986/87)
Numerische Mathematik
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Natural Runge-Kutta and Projection Methods.
Marino Zennaro (1988)
Numerische Mathematik
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Partitioned Adaptive Runge-Kutta Methods and Their Stability.
K. Strehmel, R. Weiner (1984)
Numerische Mathematik
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Partitioned Runge-Kutta Methods with Stiffness Detection and Stepsize Control.
Peter Rentrop (1985)
Numerische Mathematik
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Time discretizations for evolution problems
Miloslav Vlasák (2017)
Applications of Mathematics
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The aim of this work is to give an introductory survey on time discretizations for liner parabolic problems. The theory of stability for stiff ordinary differential equations is explained on this problem and applied to Runge-Kutta and multi-step discretizations. Moreover, a natural connection between Galerkin time discretizations and Runge-Kutta methods together with order reduction phenomenon is discussed.
Monotonicity and Boundedness in Implicit Runge-Kutta Methods.
M.N. Spijker (1986/87)
Numerische Mathematik
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The application of a class of one-step methods to solve the initial value problem
M. Szyszkowicz (1987)
Applicationes Mathematicae
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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.