Scilab Function

impl - differential algebraic equation

### Parameters

• y0,ydot0 : real vectors or matrix (initial conditions).
• t0 : real scalar (initial time).
• t : 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 scalar or real vector of the same size as as y.
• jac : external (function or character string or list).

### Description

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. r 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 SCIDIR/routines/default/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 SCIDIR/routines/default/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 adda 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 SCIDIR/routines/default/Ex-impl.f for an example to do that.

jac can also be a list: see the help of ode.

### Examples

```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);
//maxi(abs(x1-x))
```