Displaying similar documents to “Construction of explicit and generalized Runge-Kutta formulas of arbitrary order with rational parameters”

A contribution to Runge-Kutta formulas of the 7th order with rational coefficients for systems of differential equations of the first order

Anton Huťa, Vladimír Penjak (1984)

Aplikace matematiky

Similarity:

The purpose of this article is to find the 7th order formulas with rational parameters. The formulas are of the 11th stage. If we compare the coefficients of the development ∑ i = 1 ∞ h i i ! d i - 1 d x i - 1 𝐟 x , 𝐲 ( x ) up to h 7 with the development given by successive insertion into the formula h . f i ( k 0 , k 1 , ... , k i - 1 ) for i = 1 , 2 , ... , 10 and k = ∑ i = 0 10 p i , k i we obtain a system of 59 condition equations with 65 unknowns (except, the 1st one, all equations are nonlinear). As the solution of this system we get the parameters of the 7th order Runge-Kutta formulas as rational numbers. ...

Generalized periodic overimplicit multistep methods (GPOM methods)

Hassan Nasr Ahmed Ismail (1979)

Aplikace matematiky

Similarity:

The paper deals with some new methods for the numerical solution of initial value problems for ordinary differential equations. The main idea of these methods consists in the fact that in one step of the method a group of unknown values of the approximate solution is computed simultaneously. The class of methods under investigation is wide enough to contain almost all known classical methods. Sufficient conditions for convergence are found.

On total truncation error estimation for the one-step method

Anna Valková (1987)

Aplikace matematiky

Similarity:

In this paper the author establishes estimation of the total truncation error after s steps in the fifth order Ruge-Kutta-Huťa formula for systems of differential equations. The approach is analogous to that used by Vejvoda for the estimation of the classical formulas of the Runge-Kutta type of the 4-th order.