Mercurial > octave-nkf
comparison scripts/ode/ode45.m @ 20580:25623ef2ff4f
doc: Rewrite docstrings for ode* family of functions.
* scripts/ode/module.mk: Remove extra newline.
* ode45.m, odeget.m, odeset.m: Rewrite docstrings.
* AbsRel_Norm.m, fuzzy_compare.m, hermite_quartic_interpolation.m,
integrate_adaptive.m, integrate_const.m, integrate_n_steps.m, kahan.m,
ode_struct_value_check.m, odepkg_event_handle.m, odepkg_structure_check.m,
runge_kutta_45_dorpri.m, starting_stepsize.m:
Don't break @deftypefn lines. Wrap lines at 80 columns rather than 72.
| author | Rik <rik@octave.org> |
|---|---|
| date | Sat, 03 Oct 2015 21:03:16 -0700 |
| parents | 3339c9bdfe6a |
| children | e368ce72a844 |
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| 20579:52ce821a52fd | 20580:25623ef2ff4f |
|---|---|
| 17 ## You should have received a copy of the GNU General Public License | 17 ## You should have received a copy of the GNU General Public License |
| 18 ## along with Octave; see the file COPYING. If not, see | 18 ## along with Octave; see the file COPYING. If not, see |
| 19 ## <http://www.gnu.org/licenses/>. | 19 ## <http://www.gnu.org/licenses/>. |
| 20 | 20 |
| 21 ## -*- texinfo -*- | 21 ## -*- texinfo -*- |
| 22 ## @deftypefn {Function File} {[@var{sol}] =} ode45 (@var{fun}, @var{slot}, @var{init}, [@var{opt}], [@var{par1}, @var{par2}, @dots{}]) | 22 ## @deftypefn {Function File} {[@var{t}, @var{y}] =} ode45 (@var{fun}, @var{trange}, @var{init}) |
| 23 ## @deftypefnx {Function File} {[@var{t}, @var{y}, [@var{xe}, @var{ye}, @var{ie}]] =} ode45 (@var{fun}, @var{slot}, @var{init}, [@var{opt}], [@var{par1}, @var{par2}, @dots{}]) | 23 ## @deftypefnx {Function File} {[@var{t}, @var{y}] =} ode45 (@var{fun}, @var{trange}, @var{init}, @var{opt}) |
| 24 ## | 24 ## @deftypefnx {Function File} {[@var{t}, @var{y}] =} ode45 (@dots{}, @var{par1}, @var{par2}, @dots{}) |
| 25 ## This function file can be used to solve a set of non--stiff ordinary | 25 ## @deftypefnx {Function File} {[@var{t}, @var{y}, @var{xe}, @var{ye}, @var{ie}] =} ode45 (@dots{}) |
| 26 ## differential equations (non--stiff ODEs) with the well known explicit | 26 ## @deftypefnx {Function File} {@var{sol} =} ode45 (@var{fun}, @var{trange}, @var{init}, @dots{}) |
| 27 ## Dormand-Prince method of order 4. | 27 ## |
| 28 ## | 28 ## Solve a set of non-stiff Ordinary Differential Equations (non-stiff ODEs) |
| 29 ## This function can be called with two output arguments: @var{t} and @var{y}. | 29 ## with the well known explicit Dormand-Prince method of order 4. |
| 30 ## Variable @var{t} is a column vector and contains the time stamps, instead | 30 ## |
| 31 ## @var{y} is a matrix in which each column refers to a different unknown of | 31 ## The first input argument must be a function handle or inline function that |
| 32 ## the problem and the rows number is the same of @var{t} rows number so that each | 32 ## defines the ODE: @code{y' = f(t,y)}. The function must accept two inputs |
| 33 ## row of @var{y} contains the values of all unknowns at the time value contained | 33 ## where the first is time @var{t} and the second is a column vector of |
| 34 ## in the corresponding row in @var{t}. | 34 ## unknowns @var{y}. |
| 35 ## | 35 ## |
| 36 ## The first input argument must be a function_handle or an inline function that | 36 ## @var{trange} specifies the time interval over which the ODE will be |
| 37 ## defines the set of ODE: @code{y' = f(t,y)}. As described above, this function | 37 ## evaluated. Usually, it is a two-element vector specifying the initial and |
| 38 ## must take two input arguments, where the first is the time and the second | 38 ## final times (@code{[tinit, tfinal]}). If there are more than two elements |
| 39 ## the unknowns, and must have just one output argument. | 39 ## then the solution will also be evaluated at these intermediate time |
| 40 ## | 40 ## instances unless the integrate function called is |
| 41 ## The second input argument must contain time informations. Usually it should | 41 ## @command{integrate_n_steps}. If there is only one time value, then |
| 42 ## be a vector with at least two elements which define the initial and the final | 42 ## @code{ode45} will raise an error unless the options structure has |
| 43 ## time instants; if the elements are more than two, then the solution will be | 43 ## non-empty fields named @var{"TimeStepNumber"} and @var{"TimeStepSize"}. |
| 44 ## evaluated also at these intermediate time instants unless the integrate function | 44 ## If the option @var{"TimeStepSize"} is not empty, then the stepper called |
| 45 ## called is the @command{integrate_n_steps}. If there is only one time value, | 45 ## will be @command{integrate_const}. If @var{"TimeStepNumber"} is also |
| 46 ## then it will give an error unless the options structure has no empty fields | 46 ## specified then the integrate function @command{integrate_n_steps} will be |
| 47 ## named @var{"TimeStepNumber"} and @var{"TimeStepSize"}. If the option | 47 ## used; otherwise, @command{integrate_adaptive} is used. For this last |
| 48 ## @var{"TimeStepSize"} is not empty, then the stepper called will be | 48 ## possibility the user can set the tolerance for the timestep computation by |
| 49 ## @command{integrate_const}, if also @var{"TimeStepNumber"} is not empty it will | 49 ## changing the option @var{"Tau"}, that has a default value of @math{1e-6}. |
| 50 ## be called the integrate function @command{integrate_n_steps}, otherwise it will | 50 ## |
| 51 ## be called @command{integrate_adaptive}. For this last possibility the user can | 51 ## The third input argument @var{init} contains the initial value for the |
| 52 ## set the tolerance for the timestep computation by setting a value to the option | 52 ## unknowns. If this is a row vector then the solution @var{y} will be a matrix |
| 53 ## @var{"Tau"}, that as default value has @math{1.e-6}. | 53 ## in which each column is the solution for the corresponding initial value |
| 54 ## | 54 ## in @var{init}. |
| 55 ## The third input argument must contain the initial value for the unknown. | 55 ## |
| 56 ## If this is a vector then the solution @var{y} will be a matrix in which each | 56 ## If present, the fourth input argument specifies options to the ODE solver. |
| 57 ## column is the solution for the corresponding initial value in @var{init}. | 57 ## It is a structure typically generated by @code{odeset}. |
| 58 ## | 58 ## |
| 59 ## The fourth input argument is not mandatory and it should contain a structure | 59 ## The function usually produces just two outputs. Variable @var{t} is a |
| 60 ## with valid ODE fields. | 60 ## column vector and contains the times where the solution was found. The |
| 61 ## output @var{y} is a matrix in which each column refers to a different | |
| 62 ## unknown of the problem and each row corresponds to a time in @var{t}. | |
| 61 ## | 63 ## |
| 62 ## For example, solve an anonymous implementation of the Van der Pol equation | 64 ## For example, solve an anonymous implementation of the Van der Pol equation |
| 65 ## | |
| 63 ## @example | 66 ## @example |
| 67 ## @group | |
| 64 ## fvdp = @@(t,y) [y(2); (1 - y(1)^2) * y(2) - y(1)]; | 68 ## fvdp = @@(t,y) [y(2); (1 - y(1)^2) * y(2) - y(1)]; |
| 65 ## [T,Y] = ode45 (fvdp, [0 20], [2 0]); | 69 ## [T,Y] = ode45 (fvdp, [0 20], [2 0]); |
| 70 ## @end group | |
| 66 ## @end example | 71 ## @end example |
| 72 ## @seealso{odeset, odeget} | |
| 67 ## @end deftypefn | 73 ## @end deftypefn |
| 68 ## | |
| 69 | 74 |
| 70 function [varargout] = ode45 (vfun, vslot, vinit, varargin) | 75 function [varargout] = ode45 (vfun, vslot, vinit, varargin) |
| 71 | 76 |
| 72 vorder = 5; % runge_kutta_45_dorpri uses local extrapolation | 77 vorder = 5; % runge_kutta_45_dorpri uses local extrapolation |
| 73 vsolver = "ode45"; | 78 vsolver = "ode45"; |