文件列表:

Arenstorf.m (1168, 2010-01-02)
Arenstorf_dop54_dop853.m (2164, 2010-03-18)
Ballode1_dop54_dop853.m (2519, 2010-03-08)
Ballode2_dop54_dop853.m (4229, 2010-03-08)
dop54.m (33153, 2010-03-08)
dop853.m (49195, 2010-03-08)
dopget.m (1945, 2010-03-05)
dopset.m (7209, 2010-03-05)
Evol_DonneesSoleilPlanetes.m (1677, 2010-03-18)
Evol_Ephemeride 2010 Helio.txt (6225, 2010-03-18)
Evol_HighDefMinimum_dop54.m (3249, 2010-02-17)
Evol_HighDefMinimum_dop853.m (3385, 2010-02-17)
Evol_Soleilplanete_dop54_dop853.m (12150, 2010-03-18)
Evol_VitAccSoleilPlanetes.m (1749, 2010-02-12)
MassOsci.m (455, 2010-02-07)
MasstFcn.m (67, 2010-03-07)
MasstOsci.m (526, 2010-03-07)
MasstyFcn.m (96, 2010-03-07)
MasstyOsci.m (551, 2010-03-07)
Mass_dop54_dop853.m (2187, 2010-03-17)
NonNegativFcn.m (57, 2010-02-13)
NonNegativ_dop54_dop853.m (1741, 2010-02-13)
Osci.m (422, 2010-02-07)
Osci_dop54_dop853.m (6136, 2010-02-12)
VanderPol.m (549, 2010-02-12)
VanderPol_dop54_dop853.m (2278, 2010-03-18)
VanderPol_t2_y2.m (1109, 2010-03-18)
VanderPol_t2_y2_dop54_dop853.m (1122, 2010-02-17)

% --------------------------------------------------------- % % Readme.txt % % % % List of the examples used to test dop54 and dop853 % % % % Denis Bichsel % % 58 Rue des Deurres % % 2000 Neuchtel % % Tel. 41 (0) 32 730 10 16 % % email: dbichsel@infomaniak.ch % % --------------------------------------------------------- % The functions dop54 and dop853 are translation in Matlab from the Fortran code written by : E. Hairer and G. Wanner Université de Genève. % --------------------------------------------------------- % The options for dop54 and dop853 can be set with dopset and read with dopget. These function are very similar to Matalb function ode45, odeset and odeget. The allowed options are essentially the same as in Matlab. The options BDF Jacobian JConstant JPattern Refine Vectorized MvPattern MassSingular InitialSlope MaxOrder are not implemented. Remark : The following options are not implemented for ode45 in Matlab BDF Jacobian JConstant JPattern Vectorized MvPattern InitialSlope MassSingular InitialSlope MaxOrder The option "Refine" is just useless with dop54 and dop 853, because it's possible to choose all the output value for the t variable without any effect on the step size calculation. DenseOuputFcn, DenseOutputSel. Like the "OutputFcn" and "OutputSel" options, "DenseOutputFcn" and "DenseOutputSel" allow to get the t and y values after each step calculation. More, with this option the user gets also the coefficients which allow dense calculation on the intervalle [t, t+h], h = step size, 5 coefficients for dop54 and 8 coefficients for dop853 (see example below). These options allows for example, the calculation with high precision of the extrema of a function % --------------------------------------------------------- % List of examples: ------------------ The name of the main function of the examples end always with "_dop54_dop853.m". The other functions with a name which begin on the same way, are used for the calculation. For example : Arenstorf_dop54_dop853.m uses the function "Arenstorf.m" Arenstorf_dop54_dop853.m This function tests the following options: RelTol AbsTol MaxIter MaxStep and compare the execution time of dop54, dop853 and Matlab ode45 Ballode1_dop54_dop853.m Ballode2_dop54_dop853.m These functions test the following options: Events OutputFcn OutputSel InitialStep MaxStep Evol_Soleilplanete_dop54_dop853.m This function tests the following options: RelTol AbsTol InitialStep MaxStep Stats DenseOutputFcn DenseOutputSel This function shows very clearly the difference of dop54 and dop853 in solving the Mercury's perihelion problem. dop54 like ode45 don't succeed but dop853 result is 531.88 arc second (true value is 531.54 in the Newton's theory) Mass_dop54_dop853.m This function tests the following options: Mass MStateDependence NonNegativ_dop54_dop853.m This function tests the following option: NonNegative Osci_dop54_dop853.m This very simple function compare the time needed in solving the same problem (harmonic oscillator) by dop54, dop853 and the Matlab function ode45. VanderPol_dop54_dop853.m This function tests the following options: OutputSel DenseOutputFcn DenseOutputSel InitialStep MaxStep % --------------------------------------------------------- %

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