Mercurial > octave-nkf
view scripts/ode/private/starting_stepsize.m @ 20568:fcb792acab9b
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 |
parents | |
children | 6256f6e366ac |
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## Copyright (C) 2013, Roberto Porcu' <roberto.porcu@polimi.it> ## OdePkg - A package for solving ordinary differential equations and more ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 2 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; If not, see <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Command} {[@var{h}] =} starting_stepsize (@var{order}, ## @var{@@fun}, @var{t0}, @var{x0}) ## ## This function file can be used to determine a good initial step for an ODE ## solver of order @var{order}. The algorithm is that one described in [1]. ## ## Second input argument, which is @var{@@fun}, is the function describing ## the differential equations, @var{t0} is the initial time and @var{x0} ## is the initial condition. ## ## This function returns a good guess for the initial timestep @var{h}. ## ## References: ## [1] E. Hairer, S.P. Norsett and G. Wanner, ## "Solving Ordinary Differential Equations I: Nonstiff Problems", Springer. ## @end deftypefn ## ## @seealso{odepkg} function h = starting_stepsize (order, func, t0, x0, AbsTol, RelTol, normcontrol) ## compute norm of initial conditions d0 = AbsRel_Norm (x0, x0, AbsTol, RelTol, normcontrol); ## compute norm of the function evaluated at initial conditions y = func (t0, x0); d1 = AbsRel_Norm (y, y, AbsTol, RelTol, normcontrol); if (d0 < 1.e-5 || d1 < 1.e-5) h0 = 1.e-6; else h0 = .01 * (d0 / d1); endif ## compute one step of Explicit-Euler x1 = x0 + h0 * y; ## approximate the derivative norm d2 = (1 / h0) * ... AbsRel_Norm (func (t0+h0, x1) - y, func (t0+h0, x1) - y, AbsTol, RelTol, normcontrol); if (max(d1, d2) <= 1.e-15) h1 = max (1.e-6, h0*1.e-3); else h1 = (1.e-2 / max (d1, d2)) ^(1 / (order+1)); endif h = min (100*h0, h1); endfunction ## Local Variables: *** ## mode: octave *** ## End: ***