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- Runge–Kutta methods - Wikipedia
In numerical analysis, the Runge–Kutta methods (English: ˈ r ʊ ŋ ə ˈ k ʊ t ɑː ⓘ RUUNG-ə-KUUT-tah [1]) are a family of implicit and explicit iterative methods, which include the Euler method, used in temporal discretization for the approximate solutions of simultaneous nonlinear equations [2]
- Runge–Kutta interpolants for high precision computations - Springer
Runge–Kutta (RK) pairs furnish approximations of the solution of an initial value problem at discrete points in the interval of integration Many techniques for enriching these methods with continuous approximations have been proposed
- Intermediate values (interpolation) after Runge-Kutta calculation
I have a numerical ODE simulation that I computed at fixed time step $h$ using a 4-th order Runge-Kutta method (RK4), producing a series of results $(x_1,y_1), (x_2,y_2), (x_3,y_3) \dots (x_N,y_N)$ If I want to find an approximate solution $y$ at a location $x$ in between my intervals, I could use
- Interpolation for Runge-Kutta Methods - JSTOR
In this paper we present a form of interpolation for Runge-Kutta methods which is applicable to some important formulas and which is not subject to the objections raised in this section
- A fifth-order interpolant for the Dormand and Prince Runge-Kutta method . . .
Some numerical experiments with the nonstiff DETEST problems show that the proposed optimal method has a good interpolatory behavior Keywords: Ordinary differential equations, Runge-Kutta methods, interpolation 1 Introduction In the last decade a number of efficient Runge-Kutta codes have been written for the numerical solution of ODEs
- Runge-Kutta and Collocation Methods
• Define Runge-Kutta methods • Introduce collocation methods • Identify collocation methods as Runge-Kutta methods • Find conditions to determine, of what order collocation methods are Geometrical Numetric Integration – p 2
- Interpolation for Runge–Kutta Methods | SIAM Journal on Numerical Analysis
Runge–Kutta methods provide a popular way to solve the initial value problem for a system of ordinary differential equations In contrast to the Adams methods, there is no natural way to approximate the solution between mesh points
- Interpolants for Runge-Kutta formulas | ACM Transactions on . . .
A general procedure for the construction of interpolants for Runge-Kutta (RK) formulas is presented As illustrations, this approach is used to develop interpolants for three explicit RK formulas, including those employed in the well-known subroutines RKF45 and DVERK
- Runge-Kutta interpolants for high precision computations.
Runge-Kutta interpolants for high precision computations Abstract Runge-Kutta (RK) pairs furnish approximations of the solution of an initial value problem at discrete points in the interval of integration Many techniques for enriching these methods with continuous approximations have been proposed
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