differential algebraic equation
y=impl([type],y0,ydot0,t0,t [,atol, [rtol]],res,adda [,jac])
real vectors or matrices (initial conditions)
a real scalar (initial time)
a real vector (times at which the solution is computed)
externals (function or character string or list)
string 'adams' or 'stiff'
real scalars or real vectors of the same size as y
external (function or character string or list).
Solution of the linear implicit differential equation
A(t,y) dy/dt=g(t,y), y(t0)=y0
t0 is the initial instant, y0
is the vector of initial conditions. Vector ydot0 of the
time derivative of y at t0 must also
be given. The input res is an external i.e. a
function with specified syntax, or the name a Fortran subroutine or a C
function (character string) with specified syntax or a
list.
If res is a function, its syntax must be as
follows:
r = res(t,y,ydot)
where t is a real scalar (time) and
y and ydot are real vector (state
and derivative of the state). This function must return
r=g(t,y)-A(t,y)*ydot.
If res is a character string, it refers to the
name of a Fortran subroutine or a C function. See
SCI/modules/differential_equations/sci_gateway/fortran/Ex-impl.f for an example to do
that.
res can also be a list: see the help of ode.
The input adda is also an external.
If adda is a function, its syntax must be as
follows:
r = adda(t,y,p)
and it must return r=A(t,y)+p where
p is a matrix to be added to
A(t,y).
If adda is a character string, it refers to the
name of a Fortran subroutine or a C function. See
SCI/modules/differential_equations/sci_gateway/fortran/Ex-impl.f for an example to do
that.
adda can also be a list: see the help of ode.
The input jac is also an external.
If jac is a function, its syntax must be as
follows:
j = jac(t,y,ydot)
and it must return the Jacobian of
r=g(t,y)-A(t,y)*ydot with respect to
y.
If jac is a character string, it refers to the
name of a Fortran subroutine or a C function. See
SCI/modules/differential_equations/sci_gateway/fortran/Ex-impl.f for an example to do
that.
jac can also be a list: see the help of ode.
y=impl([1;0;0],[-0.04;0.04;0],0,0.4,'resid','aplusp'); // Using hot restart //[x1,w,iw]=impl([1;0;0],[-0.04;0.04;0],0,0.2,'resid','aplusp'); // hot start from previous call //[x1]=impl([1;0;0],[-0.04;0.04;0],0.2,0.4,'resid','aplusp',w,iw); //max(abs(x1-x)) |  |  |