differential algebraic equation
y=impl([type],y0,ydot0,t0,t [,atol, [rtol]],res,adda [,jac])
:y0, ydot0 real vectors or matrices (initial conditions) : :t0 a real scalar (initial time) : :t a real vector (times at which the solution is computed) : :res, adda externals (function or character string or list) : :type string ‘adams’ or ‘stiff’ : :atol, rtol real scalars or real vectors of the same size as y : :jac 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 calling sequence 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))