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• Dormand–Prince_method abstract "In numerical analysis, the Dormand–Prince (RKDP) method or DOPRI method, is an explicit 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 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 Cash–Karp (RKCK).The Dormand–Prince method has seven stages, but it uses only six function evaluations per step because it has the FSAL (First Same As Last) property: the last stage is evaluated at the same point as the first stage of the next step. Dormand and Prince chose the coefficients of their method to minimize the error of the fifth-order solution. This is the main difference with the Fehlberg method, which was constructed so that the fourth-order solution has a small error. For this reason, the Dormand–Prince method is more suitable when the higher-order solution is used to continue the integration, a practice known as local extrapolation (Shampine 1986; Hairer, Nørsett & Wanner 2008, pp. 178–179).Dormand–Prince is currently the default method in MATLAB and GNU Octave's ode45 solver and is the default choice for the Simulink's model explorer solver. A Fortran free software implementation of the algorithm called DOPRI5 is also available.The Butcher tableau is:The first row of b coefficients gives the fifth-order accurate solution and the second row gives the fourth-order accurate solution.".
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• Dormand–Prince_method wikiPageWikiLink Cash–Karp_method.
• Dormand–Prince_method wikiPageWikiLink Category:Numerical_differential_equations.
• Dormand–Prince_method wikiPageWikiLink Category:Runge–Kutta_methods.
• Dormand–Prince_method wikiPageWikiLink Fortran.
• Dormand–Prince_method wikiPageWikiLink Free_software.
• Dormand–Prince_method wikiPageWikiLink GNU_Octave.
• Dormand–Prince_method wikiPageWikiLink MATLAB.
• Dormand–Prince_method wikiPageWikiLink Mathematics_of_Computation.
• Dormand–Prince_method wikiPageWikiLink Numerical_analysis.
• Dormand–Prince_method wikiPageWikiLink Ordinary_differential_equation.
• Dormand–Prince_method wikiPageWikiLink Python_(programming_language).
• Dormand–Prince_method wikiPageWikiLink Runge–Kutta_methods.
• Dormand–Prince_method wikiPageWikiLink Runge–Kutta–Fehlberg_method.
• Dormand–Prince_method wikiPageWikiLink Simulink.
• Dormand–Prince_method wikiPageWikiLink Springer_Science+Business_Media.
• Dormand–Prince_method wikiPageWikiLinkText "Dormand–Prince method".
• Dormand–Prince_method wikiPageWikiLinkText "Dormand–Prince".
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• Dormand–Prince_method subject Category:Numerical_differential_equations.
• Dormand–Prince_method subject Category:Runge–Kutta_methods.
• Dormand–Prince_method hypernym Method.
• Dormand–Prince_method type Software.
• Dormand–Prince_method type Redirect.
• Dormand–Prince_method comment "In numerical analysis, the Dormand–Prince (RKDP) method or DOPRI method, is an explicit 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 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.".
• Dormand–Prince_method label "Dormand–Prince method".
• Dormand–Prince_method sameAs Q5298067.
• Dormand–Prince_method sameAs Método_de_Dormand-Prince.
• Dormand–Prince_method sameAs Método_de_Dormand-Prince.
• Dormand–Prince_method sameAs m.0273ydp.
• Dormand–Prince_method sameAs Q5298067.
• Dormand–Prince_method wasDerivedFrom Dormand–Prince_method?oldid=683434127.
• Dormand–Prince_method isPrimaryTopicOf Dormand–Prince_method.