Solver for Fully Implicit ODEs :: Differential Equations (Mathematics)

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,...,tf].

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.

`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.

`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