# Owl-ODE¶

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Github: {Signature} {Implementation}

val odeint : (module Types.SolverT with type output = 'a and type s = 'b and type t = 'c) -> ('b -> float -> 'c) -> 'b -> Types.tspec_t -> unit -> 'a


odeint (module Solver) f y0 timespec () numerically integrates an initial value problem for a system of ODEs given an initial value:

$\frac{dy}{dt} = f(y,t)$
$y(t_{0}) = y_{0}$

Here $$t$$ is a one-dimensional independent variable (time), $$y(t)$$ is an n-dimensional vector-valued function (state), and the n-dimensional vector-valued function $$f(y, t)$$ determines the differential equations.

The goal is to find $$y(t)$$ approximately satisfying the differential equations, given an initial value $$y(t_{0}) = y_{0}$$. The time $$t_{0}$$ is passed as part of the timespec, that includes also the final integration time and a time step. Refer to {!Owl_ode.Types.tspec_t} for further information.

The solver has to be passed as a first-class module and have a common type, {!Owl_ode.Types.SolverT}. This is useful to write new custom solvers or extend and customise the provided ones.

Refer to the documentation of the {!Owl_ode.Types.SolverT} type for further information.

source code