Cash–Karp method

Cash–Karp method

In numerical analysis, the Cash–Karp method is a method for solving ordinary differential equations (ODEs). The method is a member of the Runge–Kutta family of ODE solvers. More specifically, it uses six function evaluations to calculate fourth- and fifth-order accurate solutions. The difference between these solutions is then taken to be the error of the (fourth order) solution. This error estimate is very convenient for adaptive stepsize integration algorithms. Other similar integration methods are Fehlberg (RKF) and Dormand–Prince (RKDP).

The Butcher tableau is:

The first row of "b" coefficients gives the fifth-order accurate solution, and the second row has order four.

References

* J. R. Cash, A. H. Karp. "A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides", "ACM Transactions on Mathematical Software" 16: 201-222, 1990. doi|10.1145/79505.79507.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем сделать НИР

Look at other dictionaries:

  • Dormand–Prince method — In numerical analysis, the Dormand–Prince method, or DOPRI method, is a method for solving ordinary differential equations (Dormand Prince 1980). The method is a member of the Runge–Kutta family of ODE solvers. More specifically, it uses six… …   Wikipedia

  • List of numerical analysis topics — This is a list of numerical analysis topics, by Wikipedia page. Contents 1 General 2 Error 3 Elementary and special functions 4 Numerical linear algebra …   Wikipedia

  • Runge–Kutta methods — In numerical analysis, the Runge–Kutta methods (pronounced IPA|/ˌʀuŋgeˈkuta/) are an important family of implicit and explicit iterative methods for the approximation of solutions of ordinary differential equations. These techniques were… …   Wikipedia

  • List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia

  • Adaptive stepsize — is a technique in numerical analysis used for many problems, but mainly for integration; This can be normal integration (that is quadrature ), or the process of solving an ordinary differential equation. This article focuses on the latter. For an …   Wikipedia

  • Método de Dormand-Prince — En análisis numérico, Dormand Prince es un método para la resolución de ecuaciones diferenciales ordinarias. Pertenece a la familia de métodos Runge Kutta. Evalúa seis veces la función para calcular las soluciones de cuarto y quinto orden. La… …   Wikipedia Español

  • performing arts — arts or skills that require public performance, as acting, singing, or dancing. [1945 50] * * * ▪ 2009 Introduction Music Classical.       The last vestiges of the Cold War seemed to thaw for a moment on Feb. 26, 2008, when the unfamiliar strains …   Universalium

  • UNITED STATES OF AMERICA — UNITED STATES OF AMERICA, country in N. America. This article is arranged according to the following outline: introduction Colonial Era, 1654–1776 Early National Period, 1776–1820 German Jewish Period, 1820–1880 East European Jewish Period,… …   Encyclopedia of Judaism

  • anthropology — anthropological /an threuh peuh loj i keuhl/, anthropologic, adj. anthropologically, adv. /an threuh pol euh jee/, n. 1. the science that deals with the origins, physical and cultural development, biological characteristics, and social customs… …   Universalium

  • List of Russian people — The Millennium of Russia monument in Veliky Novgorod, featuring the statues and reliefs of the most celebrated people in the first 1000 years of Russian history …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”