Solve fully implicit differential equations — variable order method

`[`

also
uses the integration settings defined by `t`

,`y`

] =
ode15i(`odefun`

,`tspan`

,`y0`

,`yp0`

,`options`

)`options`

,
which is an argument created using the `odeset`

function.
For example, use the `AbsTol`

and `RelTol`

options
to specify absolute and relative error tolerances, or the `Jacobian`

option
to provide the Jacobian matrix.

`[`

additionally
finds where functions of `t`

,`y`

,`te`

,`ye`

,`ie`

]
= ode15i(`odefun`

,`tspan`

,`y0`

,`yp0`

,`options`

)`(t,y,y')`

, called event
functions, are zero. In the output, `te`

is the time
of the event, `ye`

is the solution at the time of
the event, and `ie`

is the index of the triggered
event.

For each event function, specify whether the integration is
to terminate at a zero and whether the direction of the zero crossing
matters. Do this by setting the `'Events'`

property
to a function, such as `myEventFcn`

or `@myEventFcn`

,
and creating a corresponding function: [`value`

,`isterminal`

,`direction`

]
= `myEventFcn`

(`t`

,`y`

,`yp`

).
For more information, see ODE Event Location.

returns
a structure that you can use with `sol`

= ode15i(___)`deval`

to evaluate
the solution at any point on the interval `[t0 tf]`

.
You can use any of the input argument combinations in previous syntaxes.

[1] Lawrence F. Shampine, "Solving
0 = F(t, y(t), y′(t)) in MATLAB," *Journal
of Numerical Mathematics*, Vol.10, No.4, 2002, pp. 291-310.

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