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.TH ode_root G "February 1998" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
ode_root - ordinary differential equation solver with root finding
.SH CALLING SEQUENCE
.nf
y,rd[,w,iw]=ode("root",y0,t0,t [,rtol [,atol]],f [,jac],ng,g [,w,iw])
.fi
.SH PARAMETERS
.TP 10
y0
: real vector or matrix (initial conditions).
.TP
t0
: real scalar (initial time).
.TP
t
: real vector (times at which the solution is computed).
.TP
f
: external i.e. function or character string or list.
.TP
rtol,atol
: real constants or real vectors of the same size
as \fVy\fR.
.TP
jac
: external i.e. function or character string or list.
.TP
w,iw
: real vectors.
.TP
ng
: integer.
.TP
g
: external i.e. function or character string or list.
.SH DESCRIPTION
With this syntax (first argument equal to \fV"root"\fR)
\fVode\fR
computes the solution
of the differential equation \fVdy/dt=f(t,y)\fR until the state
\fVy(t)\fR crosses the surface \fVg(t,y)=0\fR.
\fVg\fR should give the equation of the surface.
It is an external i.e. a function with
specified syntax, or the name of a Fortran subroutine or a C function
(character string) with specified calling sequence or a list.
.LP
If \fVg\fR is a function the syntax should be as follows:
.nf
z=g(t,y)
.fi
where \fVt\fR is a real scalar (time) and \fVy\fR a real vector (state).
It returns a vector of size \fVng\fR which corresponds to
the \fVng\fR constraints.
If \fVg\fR is a character string it refers to the name of a Fortran
subroutine or a C function, with the following calling sequence:
\fVg(n,t,y,ng,gout)\fR
where \fVng\fR is the number of constraints and
\fVgout\fR is the value of \fVg\fR (output of the program).
If \fVg\fR is a list the same conventions as for \fVf\fR apply (see ode
help).
Ouput \fVrd\fR is a \fV1 x k\fR vector. The first entry contains the stopping
time. Other entries indicate which components of \fVg\fR have changed
sign. \fVk\fR larger than 2 indicates that more than one surface
(\fV(k-1)\fR surfaces) have been simultaneously traversed.
Other arguments and other options are the same as for \fVode\fR, see the
ode help.
.SH EXAMPLE
.nf
// Integration of the differential equation
// dy/dt=y , y(0)=1, and finds the minimum time t such that y(t)=2
deff("[ydot]=f(t,y)","ydot=y")
deff("[z]=g(t,y)","z=y-2")
y0=1;ng=1;
[y,rd]=ode("roots",y0,0,2,f,ng,g)
deff("[z]=g(t,y)","z=y-[2;2;33]")
[y,rd]=ode("roots",1,0,2,f,3,g)
.fi
.SH SEE ALSO
dasrt, ode
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