octave-nkf: doc/interpreter/diffeq.txi annotate

annotate doc/interpreter/diffeq.txi @ 20606:1b62fc4e1b2f stable

doc: Cuddle parentheses in example code of for loop. * stmt.txi: Cuddle parentheses in example code of for loop.

author	Rik <rik@octave.org>
date	Wed, 07 Oct 2015 14:41:39 -0700
parents	4197fc428c7d
children	fcb792acab9b

rev	line source
19731 4197fc428c7d maint: Update copyright notices for 2015. John W. Eaton <jwe@octave.org> parents: 19630 diff changeset	1 @c Copyright (C) 1996-2015 John W. Eaton
7018 fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6778 diff changeset	2 @c
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6778 diff changeset	3 @c This file is part of Octave.
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6778 diff changeset	4 @c
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6778 diff changeset	5 @c Octave is free software; you can redistribute it and/or modify it
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6778 diff changeset	6 @c under the terms of the GNU General Public License as published by the
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6778 diff changeset	7 @c Free Software Foundation; either version 3 of the License, or (at
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6778 diff changeset	8 @c your option) any later version.
19627 446c46af4b42 strip trailing whitespace from most source files John W. Eaton <jwe@octave.org> parents: 17744 diff changeset	9 @c
7018 fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6778 diff changeset	10 @c Octave is distributed in the hope that it will be useful, but WITHOUT
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6778 diff changeset	11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6778 diff changeset	12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6778 diff changeset	13 @c for more details.
19627 446c46af4b42 strip trailing whitespace from most source files John W. Eaton <jwe@octave.org> parents: 17744 diff changeset	14 @c
7018 fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6778 diff changeset	15 @c You should have received a copy of the GNU General Public License
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6778 diff changeset	16 @c along with Octave; see the file COPYING. If not, see
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6778 diff changeset	17 @c <http://www.gnu.org/licenses/>.
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	18
4167 aae05d51353c [project @ 2002-11-12 02:52:50 by jwe] jwe parents: 4115 diff changeset	19 @node Differential Equations
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	20 @chapter Differential Equations
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	21
6700 b55d109ffe7e [project @ 2007-06-12 20:51:47 by jwe] jwe parents: 5173 diff changeset	22 Octave has built-in functions for solving ordinary differential equations,
b55d109ffe7e [project @ 2007-06-12 20:51:47 by jwe] jwe parents: 5173 diff changeset	23 and differential-algebraic equations.
8828 8463d1a2e544 Doc fixes. Brian Gough <bjg@network-theory.co.uk> parents: 8286 diff changeset	24 All solvers are based on reliable ODE routines written in Fortran.
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	25
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	26 @menu
17152 f2a8592b8fbd doc: Shorten some long subsection names in Manual. Rik <rik@octave.org> parents: 16868 diff changeset	27 * Ordinary Differential Equations::
f2a8592b8fbd doc: Shorten some long subsection names in Manual. Rik <rik@octave.org> parents: 16868 diff changeset	28 * Differential-Algebraic Equations::
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	29 @end menu
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	30
12578 f5a780d675a1 Clean up operator and function indices in documentation. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	31 @cindex differential equations
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	32 @cindex ODE
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	33 @cindex DAE
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	34
4167 aae05d51353c [project @ 2002-11-12 02:52:50 by jwe] jwe parents: 4115 diff changeset	35 @node Ordinary Differential Equations
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	36 @section Ordinary Differential Equations
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	37
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	38 The function @code{lsode} can be used to solve ODEs of the form
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	39 @tex
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	40 $$
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	41 {dx\over dt} = f (x, t)
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	42 $$
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	43 @end tex
10668 72585f1ca7a2 Replace @ifinfo with @ifnottex. Rik <octave@nomad.inbox5.com> parents: 9209 diff changeset	44 @ifnottex
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	45
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	46 @example
9067 8970b4b10e9f Cleanup documentation for quad.texi and diffeq.texi Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	47 @group
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	48 dx
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	49 -- = f (x, t)
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	50 dt
9067 8970b4b10e9f Cleanup documentation for quad.texi and diffeq.texi Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	51 @end group
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	52 @end example
10828 322f43e0e170 Grammarcheck .txi documentation files. Rik <octave@nomad.inbox5.com> parents: 10668 diff changeset	53
10668 72585f1ca7a2 Replace @ifinfo with @ifnottex. Rik <octave@nomad.inbox5.com> parents: 9209 diff changeset	54 @end ifnottex
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	55
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	56 @noindent
19074 0850b5212619 doc: Add @nospell macro around proper names in documentation. Rik <rik@octave.org> parents: 17744 diff changeset	57 using @nospell{Hindmarsh's} ODE solver @sc{lsode}.
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	58
6700 b55d109ffe7e [project @ 2007-06-12 20:51:47 by jwe] jwe parents: 5173 diff changeset	59
b55d109ffe7e [project @ 2007-06-12 20:51:47 by jwe] jwe parents: 5173 diff changeset	60
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3294 diff changeset	61 @DOCSTRING(lsode)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	62
4115 fc2048d4cd21 [project @ 2002-10-22 21:28:42 by jwe] jwe parents: 3373 diff changeset	63 @DOCSTRING(lsode_options)
fc2048d4cd21 [project @ 2002-10-22 21:28:42 by jwe] jwe parents: 3373 diff changeset	64
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	65 Here is an example of solving a set of three differential equations using
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	66 @code{lsode}. Given the function
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	67
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	68 @cindex oregonator
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	69
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	70 @example
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	71 @group
16868 b028df1b1e81 doc: Mention oregonator.m in examples dir in documentation. Rik <rik@octave.org> parents: 14856 diff changeset	72 ## oregonator differential equation
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	73 function xdot = f (x, t)
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	74
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	75 xdot = zeros (3,1);
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	76
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	77 xdot(1) = 77.27 * (x(2) - x(1)*x(2) + x(1) \
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	78 - 8.375e-06*x(1)^2);
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	79 xdot(2) = (x(3) - x(1)*x(2) - x(2)) / 77.27;
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	80 xdot(3) = 0.161*(x(1) - x(3));
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	81
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	82 endfunction
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	83 @end group
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	84 @end example
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	85
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	86 @noindent
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	87 and the initial condition @code{x0 = [ 4; 1.1; 4 ]}, the set of
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	88 equations can be integrated using the command
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	89
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	90 @example
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	91 @group
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	92 t = linspace (0, 500, 1000);
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	93
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	94 y = lsode ("f", x0, t);
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	95 @end group
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	96 @end example
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	97
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	98 If you try this, you will see that the value of the result changes
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	99 dramatically between @var{t} = 0 and 5, and again around @var{t} = 305.
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	100 A more efficient set of output points might be
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	101
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	102 @example
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	103 @group
14856 c3fd61c59e9c maint: Use Octave coding conventions for cuddling parentheses in doc directory Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	104 t = [0, logspace(-1, log10(303), 150), \
c3fd61c59e9c maint: Use Octave coding conventions for cuddling parentheses in doc directory Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	105 logspace(log10(304), log10(500), 150)];
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	106 @end group
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	107 @end example
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	108
19074 0850b5212619 doc: Add @nospell macro around proper names in documentation. Rik <rik@octave.org> parents: 17744 diff changeset	109 See @nospell{Alan C. Hindmarsh},
0850b5212619 doc: Add @nospell macro around proper names in documentation. Rik <rik@octave.org> parents: 17744 diff changeset	110 @cite{ODEPACK, A Systematized Collection of ODE Solvers},
0850b5212619 doc: Add @nospell macro around proper names in documentation. Rik <rik@octave.org> parents: 17744 diff changeset	111 in Scientific Computing, @nospell{R. S. Stepleman}, editor, (1983)
0850b5212619 doc: Add @nospell macro around proper names in documentation. Rik <rik@octave.org> parents: 17744 diff changeset	112 for more information about the inner workings of @code{lsode}.
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	113
16868 b028df1b1e81 doc: Mention oregonator.m in examples dir in documentation. Rik <rik@octave.org> parents: 14856 diff changeset	114 An m-file for the differential equation used above is included with the
b028df1b1e81 doc: Mention oregonator.m in examples dir in documentation. Rik <rik@octave.org> parents: 14856 diff changeset	115 Octave distribution in the examples directory under the name
b028df1b1e81 doc: Mention oregonator.m in examples dir in documentation. Rik <rik@octave.org> parents: 14856 diff changeset	116 @file{oregonator.m}.
b028df1b1e81 doc: Mention oregonator.m in examples dir in documentation. Rik <rik@octave.org> parents: 14856 diff changeset	117
4167 aae05d51353c [project @ 2002-11-12 02:52:50 by jwe] jwe parents: 4115 diff changeset	118 @node Differential-Algebraic Equations
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	119 @section Differential-Algebraic Equations
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	120
4115 fc2048d4cd21 [project @ 2002-10-22 21:28:42 by jwe] jwe parents: 3373 diff changeset	121 The function @code{daspk} can be used to solve DAEs of the form
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	122 @tex
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	123 $$
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	124 0 = f (\dot{x}, x, t), \qquad x(t=0) = x_0, \dot{x}(t=0) = \dot{x}_0
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	125 $$
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	126 @end tex
6700 b55d109ffe7e [project @ 2007-06-12 20:51:47 by jwe] jwe parents: 5173 diff changeset	127 @ifnottex
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	128
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	129 @example
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	130 0 = f (x-dot, x, t), x(t=0) = x_0, x-dot(t=0) = x-dot_0
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	131 @end example
10828 322f43e0e170 Grammarcheck .txi documentation files. Rik <octave@nomad.inbox5.com> parents: 10668 diff changeset	132
6700 b55d109ffe7e [project @ 2007-06-12 20:51:47 by jwe] jwe parents: 5173 diff changeset	133 @end ifnottex
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	134
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	135 @noindent
6700 b55d109ffe7e [project @ 2007-06-12 20:51:47 by jwe] jwe parents: 5173 diff changeset	136 where
b55d109ffe7e [project @ 2007-06-12 20:51:47 by jwe] jwe parents: 5173 diff changeset	137 @tex
b55d109ffe7e [project @ 2007-06-12 20:51:47 by jwe] jwe parents: 5173 diff changeset	138 $\dot{x} = {dx \over dt}$
b55d109ffe7e [project @ 2007-06-12 20:51:47 by jwe] jwe parents: 5173 diff changeset	139 @end tex
b55d109ffe7e [project @ 2007-06-12 20:51:47 by jwe] jwe parents: 5173 diff changeset	140 @ifnottex
b55d109ffe7e [project @ 2007-06-12 20:51:47 by jwe] jwe parents: 5173 diff changeset	141 @math{x-dot}
b55d109ffe7e [project @ 2007-06-12 20:51:47 by jwe] jwe parents: 5173 diff changeset	142 @end ifnottex
19074 0850b5212619 doc: Add @nospell macro around proper names in documentation. Rik <rik@octave.org> parents: 17744 diff changeset	143 is the derivative of @math{x}. The equation is solved using
0850b5212619 doc: Add @nospell macro around proper names in documentation. Rik <rik@octave.org> parents: 17744 diff changeset	144 @nospell{Petzold's} DAE solver @sc{daspk}.
4115 fc2048d4cd21 [project @ 2002-10-22 21:28:42 by jwe] jwe parents: 3373 diff changeset	145
fc2048d4cd21 [project @ 2002-10-22 21:28:42 by jwe] jwe parents: 3373 diff changeset	146 @DOCSTRING(daspk)
fc2048d4cd21 [project @ 2002-10-22 21:28:42 by jwe] jwe parents: 3373 diff changeset	147
fc2048d4cd21 [project @ 2002-10-22 21:28:42 by jwe] jwe parents: 3373 diff changeset	148 @DOCSTRING(daspk_options)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	149
10828 322f43e0e170 Grammarcheck .txi documentation files. Rik <octave@nomad.inbox5.com> parents: 10668 diff changeset	150 Octave also includes @sc{dassl}, an earlier version of @sc{daspk},
322f43e0e170 Grammarcheck .txi documentation files. Rik <octave@nomad.inbox5.com> parents: 10668 diff changeset	151 and @sc{dasrt}, which can be used to solve DAEs with constraints
4115 fc2048d4cd21 [project @ 2002-10-22 21:28:42 by jwe] jwe parents: 3373 diff changeset	152 (stopping conditions).
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	153
8286 6f2d95255911 fix @seealso references to point to existing anchors Thorsten Meyer <thorsten.meyier@gmx.de> parents: 7018 diff changeset	154 @DOCSTRING(dassl)
6f2d95255911 fix @seealso references to point to existing anchors Thorsten Meyer <thorsten.meyier@gmx.de> parents: 7018 diff changeset	155
6f2d95255911 fix @seealso references to point to existing anchors Thorsten Meyer <thorsten.meyier@gmx.de> parents: 7018 diff changeset	156 @DOCSTRING(dassl_options)
6f2d95255911 fix @seealso references to point to existing anchors Thorsten Meyer <thorsten.meyier@gmx.de> parents: 7018 diff changeset	157
4115 fc2048d4cd21 [project @ 2002-10-22 21:28:42 by jwe] jwe parents: 3373 diff changeset	158 @DOCSTRING(dasrt)
fc2048d4cd21 [project @ 2002-10-22 21:28:42 by jwe] jwe parents: 3373 diff changeset	159
fc2048d4cd21 [project @ 2002-10-22 21:28:42 by jwe] jwe parents: 3373 diff changeset	160 @DOCSTRING(dasrt_options)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	161
19074 0850b5212619 doc: Add @nospell macro around proper names in documentation. Rik <rik@octave.org> parents: 17744 diff changeset	162 See @nospell{K. E. Brenan}, et al., @cite{Numerical Solution of Initial-Value
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	163 Problems in Differential-Algebraic Equations}, North-Holland (1989) for
10828 322f43e0e170 Grammarcheck .txi documentation files. Rik <octave@nomad.inbox5.com> parents: 10668 diff changeset	164 more information about the implementation of @sc{dassl}.

Mercurial > octave-nkf

annotate doc/interpreter/diffeq.txi @ 20606:1b62fc4e1b2f stable