Mercurial > octave-nkf
diff doc/interpreter/diffeq.txi @ 3373:36405da8e173
[project @ 1999-11-23 20:54:17 by jwe]
author | jwe |
---|---|
date | Tue, 23 Nov 1999 20:54:31 +0000 |
parents | bfe1573bd2ae |
children | fc2048d4cd21 |
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--- a/doc/interpreter/diffeq.txi Tue Nov 23 19:07:18 1999 +0000 +++ b/doc/interpreter/diffeq.txi Tue Nov 23 20:54:31 1999 +0000 @@ -40,29 +40,7 @@ @noindent using Hindmarsh's ODE solver @sc{Lsode}. -@deftypefn {Loadable Function} {} lsode (@var{fcn}, @var{x0}, @var{t}, @var{t_crit}) -Return a matrix of @var{x} as a function of @var{t}, given the initial -state of the system @var{x0}. Each row in the result matrix corresponds -to one of the elements in the vector @var{t}. The first element of -@var{t} corresponds to the initial state @var{x0}, so that the first row -of the output is @var{x0}. - -The first argument, @var{fcn}, is a string that names the function to -call to compute the vector of right hand sides for the set of equations. -It must have the form - -@example -@var{xdot} = f (@var{x}, @var{t}) -@end example - -@noindent -where @var{xdot} and @var{x} are vectors and @var{t} is a scalar. - -The fourth argument is optional, and may be used to specify a set of -times that the ODE solver should not integrate past. It is useful for -avoiding difficulties with singularities and points where there is a -discontinuity in the derivative. -@end deftypefn +@DOCSTRING(lsode) Here is an example of solving a set of three differential equations using @code{lsode}. Given the function @@ -107,13 +85,7 @@ @end group @end example -@deftypefn {Loadable Function} {} lsode_options (@var{opt}, @var{val}) -When called with two arguments, this function allows you set options -parameters for the function @code{lsode}. Given one argument, -@code{lsode_options} returns the value of the corresponding option. If -no arguments are supplied, the names of all the available options and -their current values are displayed. -@end deftypefn +@DOCSTRING(lsode_options) See Alan C. Hindmarsh, @cite{ODEPACK, A Systematized Collection of ODE Solvers}, in Scientific Computing, R. S. Stepleman, editor, (1983) for @@ -140,49 +112,9 @@ @noindent using Petzold's DAE solver @sc{Dassl}. -@deftypefn {Loadable Function} {[@var{x}, @var{xdot}] =} dassl (@var{fcn}, @var{x0}, @var{xdot0}, @var{t}, @var{t_crit}) -Return a matrix of states and their first derivatives with respect to -@var{t}. Each row in the result matrices correspond to one of the -elements in the vector @var{t}. The first element of @var{t} -corresponds to the initial state @var{x0} and derivative @var{xdot0}, so -that the first row of the output @var{x} is @var{x0} and the first row -of the output @var{xdot} is @var{xdot0}. - -The first argument, @var{fcn}, is a string that names the function to -call to compute the vector of residuals for the set of equations. -It must have the form - -@example -@var{res} = f (@var{x}, @var{xdot}, @var{t}) -@end example - -@noindent -where @var{x}, @var{xdot}, and @var{res} are vectors, and @var{t} is a -scalar. +@DOCSTRING(dassl) -The second and third arguments to @code{dassl} specify the initial -condition of the states and their derivatives, and the fourth argument -specifies a vector of output times at which the solution is desired, -including the time corresponding to the initial condition. - -The set of initial states and derivatives are not strictly required to -be consistent. In practice, however, @sc{Dassl} is not very good at -determining a consistent set for you, so it is best if you ensure that -the initial values result in the function evaluating to zero. - -The fifth argument is optional, and may be used to specify a set of -times that the DAE solver should not integrate past. It is useful for -avoiding difficulties with singularities and points where there is a -discontinuity in the derivative. -@end deftypefn - -@deftypefn {Loadable Function} {} dassl_options (@var{opt}, @var{val}) -When called with two arguments, this function allows you set options -parameters for the function @code{lsode}. Given one argument, -@code{dassl_options} returns the value of the corresponding option. If -no arguments are supplied, the names of all the available options and -their current values are displayed. -@end deftypefn +@DOCSTRING(dassl_options) See K. E. Brenan, et al., @cite{Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations}, North-Holland (1989) for