Runge-Kutta method
, that were develoved around 1900 by the german. mathematicians C. Runge (1856?1927) and M.W. Kutta (1867?1944).
Runge-Kutta Methods
. These methods are intended for large systems of ordinary differential equations originating mainly from semi- discretization in space of parabolic or hyperbolic-parabolic equations.
Fifth-order Runge-Kutta with higher order derivative approximations
A fourth- order method is presented which uses only two memory locations per dependent variable, while the classical fourth-order Runge?Kutta method uses three.
Diagonally Implicit Runge-Kutta Methods for Ordinary Differential ...
The Runge-Kutta methods are an important family of iterative methods for the ap- proximation of solutions of ODE's, that were develoved around 1900 by the ...
An Explicit Runge-Kutta Method of Order Twelve - Dynamic Publishers
The result is the addition of a higher derivative term to the standard Runge-Kutta method. The following describes three methods to utilize fy.
Higher order approximations of runge-kutta type
The goal of this review is to summarize the characteristics, assess the potential, and then design several nearly optimal, general purpose, DIRK-type methods.
A Tenth-Order Runge-Kutta Method with Error Estimate
The equations of condition for a twelfth-order explicit Runge-Kutta method with twenty-five stages are solved using m-symmetry. The method contains an embedded ...
A Method for the Numerical Integration of Differ
The fourth-order formula of Runge-Kutta has been used extensively to obtain approximate solutions of differential equations of first, second, ...
Stability of Runge-Kutta Methods - webspace.science.uu.nl
Runge?Kutta methods for ODEs. Taylor series. General Runge?Kutta schemes. Explicit and implicit schemes. Strong stochastic Runge?Kutta methods.
iterated runge-kutta methods on parallel computers
This is not the case for the first derivative, which is determined in the Runge-Kutta method with fifth-order accuracy; however, this fifth- order accuracy may ...
Advanced Numerical Analysis - EPFL
An A-stable numerical method has the property that the origin is stable regardless of the stepsize. Another important issue is whether the numerical method ...
Méthodes d'Euler et de Runge-Kutta
Abstract. This paper examines diagonally implicit iteration methods for solving implicit Runge-Kutta methods with high stage order on parallel computers.
Méthodes d'Euler et de Runge-Kutta
Abstract. This paper examines diagonally implicit iteration methods for solving implicit Runge-Kutta methods with high stage order on parallel computers.
Autour des méthodes de Runge-Kutta - WordPress.com
Abstract. For the solution of differential-algebraic systems, only those Runge-Kutta formulae with nonsingular coefficient matrix A have been considered up ...
Monotonicity and Boundedness in general Runge-Kutta methods
La méthode RK4 est une méthode d'ordre 4 au sens o`u l'erreur commise `a chaque étape. (Xk,Yk) ? (Xk+1,Yk+1) est de l'ordre de h5, donc l'erreur totale ...
Convergence and order reduction of diagonally implicit Runge-Kutta ...
Abstract. The Runge-Kutta method is a one step method with multiple stages, the number of stages determine order of method. The method can be applied to ...