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Efficient symplectic Runge–Kutta methods
Applied Mathematics and Computation, 2006The authors consider the efficiency of symplectic Runge-Kutta methods with real eigenvalues for the numerical integration of initial value problems for systems of ordinary differential equations.
Robert P. K. Chan +2 more
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A Note on a Runge‐Kutta‐Chebyshev Method
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1982Le but de ce travail est de présenter quelques considérations sur la solution numérique d'un problème avec valeur initiale pour des systèmes d'équations différentielles ordinaires de la forme \(y'=f(y)\), qui jouïssent de la propriété que les valeurs propres de la matrice jacobienne \(J(f)=\partial f(y)/\partial y\) sont situées sur une bande longue et
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A parallel Runge-Kutta integration method
Parallel Computing, 1989Abstract In this paper, the development of parallel integration methods of Runge-Kutta form for the step by step solution of ordinary differential equations is presented.
David J. Evans 0001, Bahrom Sanugi
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2019
The class of differential equations for which explicit solutions can be obtained is rather small. In fact, in Chap. 3, we have already remarked that to find an explicit solution of the second-order linear differential equation ( 3.2) there does not exist any method.
Ravi P. Agarwal +2 more
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The class of differential equations for which explicit solutions can be obtained is rather small. In fact, in Chap. 3, we have already remarked that to find an explicit solution of the second-order linear differential equation ( 3.2) there does not exist any method.
Ravi P. Agarwal +2 more
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Runge–Kutta–Chebyshev projection method
Journal of Computational Physics, 2006In this paper a fully explicit, stabilized projection method called the Runge-Kutta-Chebyshev (RKC) projection method is presented for the solution of incompressible Navier-Stokes systems. This method preserves the extended stability property of the RKC method for solving ODEs, and it requires only one projection per step.
Zheming Zheng, Linda R. Petzold
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1973
One-step methods (see Def. 2.1.8) form a particularly simple class of f. s. m. for IVP 1. Among these, a certain class of methods has commonly been associated with the names of C. Runge and W. Kutta and is widely used. These “Runge-Kutta methods” (RK-methods) are 1-step m+1-stage methods in the sense of Def. 2.1.10.
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One-step methods (see Def. 2.1.8) form a particularly simple class of f. s. m. for IVP 1. Among these, a certain class of methods has commonly been associated with the names of C. Runge and W. Kutta and is widely used. These “Runge-Kutta methods” (RK-methods) are 1-step m+1-stage methods in the sense of Def. 2.1.10.
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Positivity of Runge-Kutta and diagonally split Runge-Kutta methods
Applied Numerical Mathematics, 1998The author investigates positivity of general Runge-Kutta and diagonally split Runge-Kutta methods for the numerical solution of positive initial value problems for ordinary differential equations. Conditions for the maximal stepsize in term of the radius of positivity of the Runge-Kutta method which guarantees positivity are given.
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Families of Imbedded Runge–Kutta Methods
SIAM Journal on Numerical Analysis, 1979Using the s stages of an explicit Runge–Kutta method of order p, approximations of various lower orders may be obtained. A linear system of equations classifies and characterizes parameters of all properly imbedded methods.For all methods with $p = 2,3$, and some with $p = 5$, and s minimal, approximations of all lower orders may be obtained. Otherwise,
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RUN beyond the metaphor: An efficient optimization algorithm based on Runge Kutta method
Expert Systems With Applications, 2021Ali Asghar Heidari +2 more
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Strong-order conditions of Runge-Kutta method for stochastic optimal control problems
Applied Numerical Mathematics, 2020Hacer Oz Bakan +2 more
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