# decic

Compute consistent initial conditions for ode15i

## Syntax

`[y0mod,yp0mod] = decic(odefun,t0,y0,fixed_y0,yp0,fixed_yp0)[y0mod,yp0mod] = decic(odefun,t0,y0,fixed_y0,yp0,fixed_yp0,options)[y0mod,yp0mod,resnrm] = decic(odefun,t0,y0,fixed_y0,yp0,fixed_yp0...)`

## Description

`[y0mod,yp0mod] = decic(odefun,t0,y0,fixed_y0,yp0,fixed_yp0)` uses the inputs `y0` and `yp0` as initial guesses for an iteration to find output values that satisfy the requirement $f\left(t0,y0\mathrm{mod},yp0\mathrm{mod}\right)=0$, i.e., `y0mod` and `yp0mod` are consistent initial conditions. `odefun` is a function handle. The function `decic` changes as few components of the guesses as possible. You can specify that `decic` holds certain components fixed by setting ```fixed_y0(i) = 1``` if no change is permitted in the guess for `y0(i)` and 0 otherwise. `decic` interprets `fixed_y0 = []` as allowing changes in all entries. `fixed_yp0` is handled similarly.

Parameterizing Functions explains how to provide additional parameters to the function `odefun`, if necessary.

You cannot fix more than `length(y0)` components. Depending on the problem, it may not be possible to fix this many. It also may not be possible to fix certain components of `y0` or `yp0`. It is recommended that you fix no more components than necessary.

`[y0mod,yp0mod] = decic(odefun,t0,y0,fixed_y0,yp0,fixed_yp0,options)` computes as above with default tolerances for consistent initial conditions, `AbsTol` and `RelTol`, replaced by the values in options, a structure you create with the `odeset` function.

`[y0mod,yp0mod,resnrm] = decic(odefun,t0,y0,fixed_y0,yp0,fixed_yp0...)` returns the norm of `odefun(t0,y0mod,yp0mod)` as `resnrm`. If the norm seems unduly large, use `options` to decrease `RelTol` (`1e-3` by default).

## Examples

The files, `ihb1dae.m` and `iburgersode.m`, provide examples which use `decic` to solve implicit ODEs.

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