Mercurial > octave-nkf
comparison scripts/ode/private/starting_stepsize.m @ 20584:eb9e2d187ed2
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> |
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date | Sun, 04 Oct 2015 22:18:54 -0700 |
parents | 25623ef2ff4f |
children |
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20583:d746695bf494 | 20584:eb9e2d187ed2 |
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15 ## You should have received a copy of the GNU General Public License | 15 ## You should have received a copy of the GNU General Public License |
16 ## along with Octave; see the file COPYING. If not, see | 16 ## along with Octave; see the file COPYING. If not, see |
17 ## <http://www.gnu.org/licenses/>. | 17 ## <http://www.gnu.org/licenses/>. |
18 | 18 |
19 ## -*- texinfo -*- | 19 ## -*- texinfo -*- |
20 ## @deftypefn {Function File} {[@var{h}] =} starting_stepsize (@var{order}, @var{@@fun}, @var{t0}, @var{x0}) | 20 ## @deftypefn {Function File} {@var{h} =} starting_stepsize (@var{order}, @var{@@fun}, @var{t0}, @var{x0}) |
21 ## | 21 ## |
22 ## This function file can be used to determine a good initial step for an ODE | 22 ## This function file can be used to determine a good initial step for an ODE |
23 ## solver of order @var{order}. The algorithm is that one described in [1]. | 23 ## solver of order @var{order}. The algorithm is that one described in [1]. |
24 ## | 24 ## |
25 ## Second input argument, which is @var{@@fun}, is the function describing | 25 ## Second input argument, which is @var{@@fun}, is the function describing |
43 | 43 |
44 ## compute norm of the function evaluated at initial conditions | 44 ## compute norm of the function evaluated at initial conditions |
45 y = func (t0, x0); | 45 y = func (t0, x0); |
46 d1 = AbsRel_Norm (y, y, AbsTol, RelTol, normcontrol); | 46 d1 = AbsRel_Norm (y, y, AbsTol, RelTol, normcontrol); |
47 | 47 |
48 if (d0 < 1.e-5 || d1 < 1.e-5) | 48 if (d0 < 1e-5 || d1 < 1e-5) |
49 h0 = 1.e-6; | 49 h0 = 1e-6; |
50 else | 50 else |
51 h0 = .01 * (d0 / d1); | 51 h0 = .01 * (d0 / d1); |
52 endif | 52 endif |
53 | 53 |
54 ## compute one step of Explicit-Euler | 54 ## compute one step of Explicit-Euler |
57 ## approximate the derivative norm | 57 ## approximate the derivative norm |
58 d2 = (1 / h0) * ... | 58 d2 = (1 / h0) * ... |
59 AbsRel_Norm (func (t0+h0, x1) - y, | 59 AbsRel_Norm (func (t0+h0, x1) - y, |
60 func (t0+h0, x1) - y, AbsTol, RelTol, normcontrol); | 60 func (t0+h0, x1) - y, AbsTol, RelTol, normcontrol); |
61 | 61 |
62 if (max(d1, d2) <= 1.e-15) | 62 if (max(d1, d2) <= 1e-15) |
63 h1 = max (1.e-6, h0*1.e-3); | 63 h1 = max (1e-6, h0*1e-3); |
64 else | 64 else |
65 h1 = (1.e-2 / max (d1, d2)) ^(1 / (order+1)); | 65 h1 = (1e-2 / max (d1, d2)) ^(1 / (order+1)); |
66 endif | 66 endif |
67 | 67 |
68 h = min (100*h0, h1); | 68 h = min (100*h0, h1); |
69 | 69 |
70 endfunction | 70 endfunction |
71 | 71 |
72 ## Local Variables: *** | |
73 ## mode: octave *** | |
74 ## End: *** |