odeoptions set options for ode solvers

## Syntax

    odeoptions()

## Description

This function interactively displays a command which should be executed to set various options of ode solvers. The context variable `%ODEOPTIONS` sets the options.

The `ode` function checks if this variable exists and in this case it uses it. For using default values you should clear this variable. To create it you must execute the instruction `%ODEOPTIONS=odeoptions()`.

The variable `%ODEOPTIONS` is a vector with the following elements:

`[itask, tcrit, h0, hmax, hmin, jactyp, mxstep, maxordn, maxords, ixpr, ml, mu]`.

The default value is: `[1,0,0,%inf,0,2,500,12,5,0,-1,-1].`

The meaning of the elements is described below.

- `itask` sets the integration mode:
  - 1: normal computation at specified times
  - 2 : computation at mesh points (given in first row of output of `ode`)
  - 3 : one step at one internal mesh point and return
  - 4 : normal computation without overshooting `tcrit`
  - 5 : one step, without passing `tcrit`, and return
- `tcrit` critical time used only if `itask` equals 4 or 5 as described above
- `h0` first step tried
- `hmax` max step size
- `hmin` min step size
- `jactype` set jacobian properties:
  - 0: functional iterations, no jacobian used (`"adams"` or `"stiff"` only)
  - 1 : user-supplied full jacobian
  - 2 : internally generated full jacobian
  - 3: internally generated diagonal jacobian (`"adams"` or `"stiff"` only)
  - 4 : user-supplied banded jacobian (see `ml` and `mu` below)
  - 5 : internally generated banded jacobian (see `ml` and `mu` below)
- `maxordn` maximum non-stiff order allowed, at most 12
- `maxords` maximum stiff order allowed, at most 5
- `ixpr` print level, 0 or 1
- `ml`,`mu`

  If `jactype` equals 4 or 5, `ml` and `mu` are the lower and upper half-bandwidths of the banded jacobian: the band is the `i,j`'s with `i-ml` <= `j` <= `ny-1`.

  If `jactype` equals 4 the jacobian function must return a matrix `J` which is `ml+mu+1 x ny` (where `ny=dim` of `y` in `ydot=f(t,y))` such that column 1 of `J` is made of `mu` zeros followed by `df1/dy1`, `df2/dy1`, `df3/dy1`, ... (`1+ml` possibly non-zero entries), column 2 is made of `mu-1` zeros followed by `df1/dx2`, `df2/dx2`, etc.

## Examples

In the following example, we solve the Ordinary Differential Equation `dy/dt=y^2-y sin(t)+cos(t)` with the initial condition `y(0)=0` claiming the solution be stored at each mesh value.

    function ydot = f(t,y)
        ydot = y^2 - y*sin(t) + cos(t)
    endfunction
    %ODEOPTIONS = [2,0,0,%inf,0,2,500,12,5,0,-1,-1];
    y = ode(0,0,%pi,f);
    plot(y(1,:),y(2,:))
    clear %ODEOPTIONS

function ydot=f(t,y) ydot=y^2-y*sin(t)+cos(t) endfunction %ODEOPTIONS=[2,0,0,%inf,0,2,500,12,5,0,-1,-1]; y=ode(0,0,%pi,f); plot(y(1,:),y(2,:)) clear %ODEOPTIONS

## See also

- ode