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ode_root Scilab Group Scilab Function ode_root
NAME
ode_root - ordinary differential equation solver with root finding
CALLING SEQUENCE
y,rd[,w,iw]=ode("root",y0,t0,t [,rtol [,atol]],f [,jac],ng,g [,w,iw])
PARAMETERS
y0 : real vector or matrix (initial conditions).
t0 : real scalar (initial time).
t : real vector (times at which the solution is computed).
f : external i.e. function or character string or list.
rtol,atol : real constants or real vectors of the same size as y.
jac : external i.e. function or character string or list.
w,iw : real vectors.
ng : integer.
g : external i.e. function or character string or list.
DESCRIPTION
With this syntax (first argument equal to "root") ode computes the
solution of the differential equation dy/dt=f(t,y) until the state y(t)
crosses the surface g(t,y)=0. g 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.
If g is a function the syntax should be as follows:
z=g(t,y)
where t is a real scalar (time) and y a real vector (state). It returns
a vector of size ng which corresponds to the ng constraints. If g is a
character string it refers to the name of a Fortran subroutine or a C
function, with the following calling sequence: g(n,t,y,ng,gout) where ng
is the number of constraints and gout is the value of g (output of the
program). If g is a list the same conventions as for f apply (see ode
help). Ouput rd is a 1 x k vector. The first entry contains the stopping
time. Other entries indicate which components of g have changed sign. k
larger than 2 indicates that more than one surface ((k-1) surfaces) have
been simultaneously traversed. Other arguments and other options are the
same as for ode, see the ode help.
EXAMPLE
// 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)
SEE ALSO
dasrt, ode
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