منابع مشابه
On Error Estimation In General Linear Methods: Runge Kutta (Rk) And Almost Runge-Kutta (Ark) Methods
Abstract— General linear methods (GLM) apply to a large family of numerical methods for ordinary differential equations, with RungeKutta (RK) and Almost Runge-Kutta (ARK) methods as two out of a number of special cases. In this paper, we have investigated the efficacy of Richardson extrapolation (RE) technique as a means of obtaining viable and acceptable estimates of the local truncation error...
متن کاملAn error analysis of Runge-Kutta convolution quadrature
An error analysis is given for convolution quadratures based on strongly A-stable RungeKutta methods, for the non-sectorial case of a convolution kernel with a Laplace transform that is polynomially bounded in a half-plane. The order of approximation depends on the classical order and stage order of the Runge-Kutta method and on the growth exponent of the Laplace transform. Numerical experiment...
متن کاملA Fourth Order Multirate Runge-Kutta Method with Error Control
To integrate large systems of ordinary differential equations (ODEs) with disparate timescales, we present a multirate method with error control that is based on embedded, explicit Runge-Kutta (RK) formulas. The order of accuracy of such methods depends on interpolating certain solution components with a polynomial of sufficiently high degree. By analyzing the method applied to a simple test eq...
متن کاملRunge - Kutta Methods page RK 1 Runge - Kutta Methods
Literature For a great deal of information on Runge-Kutta methods consult J.C. Butcher, Numerical Methods for Ordinary Differential Equations, second edition, Wiley and Sons, 2008, ISBN 9780470723357. That book also has a good introduction to linear multistep methods. In these notes we refer to this books simply as Butcher. The notes were written independently of the book which accounts for som...
متن کاملInternal Error Propagation in Explicit Runge-Kutta Methods
In practical computation with Runge–Kutta methods, the stage equations are not satisfied exactly, due to roundoff errors, algebraic solver errors, and so forth. We show by example that propagation of such errors within a single step can have catastrophic effects for otherwise practical and well-known methods. We perform a general analysis of internal error propagation, emphasizing that it depen...
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ژورنال
عنوان ژورنال: Applications of Mathematics
سال: 1957
ISSN: 0862-7940,1572-9109
DOI: 10.21136/am.1957.102549