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ode_root(G) Scilab Function ode_root(G)
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 vector of the same size as y. 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 func-
tion with specified syntax, or the name a Fortran subroutine or a C func-
tion (character string) with specified calling sequence or a list.
If g is 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 char-
acter 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 is a list the same conventions as for f apply (see ode help).
Ouput rd is a 1xk vector. The first entry contains the stopping time. Other
entries indicate which components of g have changed sign. k larger than two
indicates that more than one surface (k-1) has 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)
SEE ALSO
dasrt, ode
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