Mathematics

Solver for Fully Implicit ODEs

The solver `ode15i` solves fully implicit differential equations of the form

using the variable order BDF method. The basic syntax for `ode15i` is

• ```[t,y] = ode15i(odefun,tspan,y0,yp0,options)
```

The input arguments are

 `odefun` A function that evaluates the left side of the differential equation of the form . `tspan` A vector specifying the interval of integration, `[t0,tf]`. To obtain solutions at specific times (all increasing or all decreasing), use `tspan = [t0,t1,...,t`f]. `y0, yp0` Vectors of initial conditions for and , respectively. The specified values must be consistent; that is, they must satisfy . Example: Solving a Fully Implicit ODE Problem shows how to use the function `decic` to compute consistent initial conditions. `options` Optional integration argument created using the `odeset` function. See the `odeset` reference page for details.

The output arguments are

 `t` Column vector of time points `y` Solution array. Each row in `y` corresponds to the solution at a time returned in the corresponding row of `t`.

See the `ode15i` reference page for more information about these arguments.

 Examples: Solving Explicit ODE Problems Example: Solving a Fully Implicit ODE Problem