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annotate scripts/ode/private/starting_stepsize.m @ 20584:eb9e2d187ed2

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maint: Use Octave coding conventions in scripts/ode/private dir. * 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: Wrap long lines to < 80 chars. Use double quotes rather than single quotes where possible. Use ';' at end of keywords "return;" and "break;" Use '##" for stand-alone comments and '#' for end-of-line comments. Use two spaces after period before starting new sentence. Use '!' instead of '~' for logical negation. Use specific form of end (endif, endfor, etc.). Don't use line continuation marker '...' unless necessary.
author Rik <rik@octave.org>
date Sun, 04 Oct 2015 22:18:54 -0700
parents 25623ef2ff4f
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 ## Copyright (C) 2013, Roberto Porcu' <roberto.porcu@polimi.it>
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {@var{h} =} starting_stepsize (@var{order}, @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} is
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27 ## 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 < 1e-5 || d1 < 1e-5)
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49 h0 = 1e-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) <= 1e-15)
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63 h1 = max (1e-6, h0*1e-3);
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64 else
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65 h1 = (1e-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