Scilab Function

impl - differential algebraic equation

### Calling Sequence

  `y=impl([type],y0,ydot0,t0,t [,atol, [rtol]],res,adda [,jac])`

### 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))

### See Also

`dassl` `ode` `external`