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annotate scripts/ode/private/starting_stepsize.m @ 20568:fcb792acab9b

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Moving ode45, odeset, odeget, and levenshtein from odepkg to core. * libinterp/corefcn/levenshtein.cc: move function from odepkg into core * libinterp/corefcn/module.mk: include levenshtein.cc * scripts/ode: move ode45, odeset, odeget, and all dependencies from odepkg into core * scripts/module.mk: include them * doc/interpreter/diffeq.txi: add documentation for ode45, odeset, odeget * NEWS: announce functions included with this changeset * scripts/help/__unimplemented__.m: removed new functions
author jcorno <jacopo.corno@gmail.com>
date Thu, 24 Sep 2015 12:58:46 +0200
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children 6256f6e366ac
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20568
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1 ## Copyright (C) 2013, Roberto Porcu' <roberto.porcu@polimi.it>
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2 ## OdePkg - A package for solving ordinary differential equations and more
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3 ##
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4 ## This program is free software; you can redistribute it and/or modify
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5 ## it under the terms of the GNU General Public License as published by
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6 ## the Free Software Foundation; either version 2 of the License, or
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7 ## (at your option) any later version.
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8 ##
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9 ## This program is distributed in the hope that it will be useful,
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10 ## but WITHOUT ANY WARRANTY; without even the implied warranty of
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11 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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12 ## GNU General Public License for more details.
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13 ##
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14 ## You should have received a copy of the GNU General Public License
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15 ## along with this program; If not, see <http://www.gnu.org/licenses/>.
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16
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17
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18 ## -*- texinfo -*-
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19 ## @deftypefn {Command} {[@var{h}] =} starting_stepsize (@var{order},
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20 ## @var{@@fun}, @var{t0}, @var{x0})
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21 ##
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22 ## This function file can be used to determine a good initial step for an ODE
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23 ## solver of order @var{order}. The algorithm is that one described in [1].
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24 ##
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25 ## Second input argument, which is @var{@@fun}, is the function describing
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26 ## the differential equations, @var{t0} is the initial time and @var{x0}
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27 ## is the initial condition.
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28 ##
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29 ## This function returns a good guess for the initial timestep @var{h}.
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30 ##
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31 ## References:
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32 ## [1] E. Hairer, S.P. Norsett and G. Wanner,
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33 ## "Solving Ordinary Differential Equations I: Nonstiff Problems", Springer.
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34 ## @end deftypefn
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35 ##
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36 ## @seealso{odepkg}
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37
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38 function h = starting_stepsize (order, func, t0, x0,
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39 AbsTol, RelTol, normcontrol)
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40
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41 ## compute norm of initial conditions
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42 d0 = AbsRel_Norm (x0, x0, AbsTol, RelTol, normcontrol);
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43
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44 ## compute norm of the function evaluated at initial conditions
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45 y = func (t0, x0);
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46 d1 = AbsRel_Norm (y, y, AbsTol, RelTol, normcontrol);
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47
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48 if (d0 < 1.e-5 || d1 < 1.e-5)
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49 h0 = 1.e-6;
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50 else
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51 h0 = .01 * (d0 / d1);
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52 endif
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53
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54 ## compute one step of Explicit-Euler
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55 x1 = x0 + h0 * y;
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56
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57 ## approximate the derivative norm
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58 d2 = (1 / h0) * ...
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59 AbsRel_Norm (func (t0+h0, x1) - y,
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60 func (t0+h0, x1) - y, AbsTol, RelTol, normcontrol);
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61
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62 if (max(d1, d2) <= 1.e-15)
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63 h1 = max (1.e-6, h0*1.e-3);
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64 else
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65 h1 = (1.e-2 / max (d1, d2)) ^(1 / (order+1));
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66 endif
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67
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68 h = min (100*h0, h1);
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69
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70 endfunction
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71
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72 ## Local Variables: ***
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73 ## mode: octave ***
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74 ## End: ***