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See the recommended documentation of this function
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])
Arguments
- 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.
Examples
<< ode_optional_output | Differential Equations, Integration | odedc >> |