package owl-ode

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Any solver compatible with Owl_ode_base.Ode.odeint has to comply with the Solver type. You can use this to define completely new solvers, as done in the owl-ode-sundials, owl-ode-odepack or ocaml-cviode libraries, or to customize pre-existing solvers (see the van_der_pol example for one such cases).

The native ocaml solvers provided by Owl_ode_base in both single and double precision can be found in Owl_ode_base.Native, respectively in the Owl_ode_base.Native.S and Owl_ode_base.Native.D modules. These provide multiple single-step and adaptive implementations.

Symplectic solvers for separable Hamiltonian systems are also available and can be found in Owl_ode_base.Symplectic.S and Owl_ode_base.Symplectic.D. Refer to the damped oscillator for an example of use.

The generic solvers in Owl_ode_base.Native_generic and in Owl_ode_base.Symplectic_generic can also be used in conjunction with jsoo, although how to do that is currently undocumented.

type state

state is the type of the state (and thus also of the initial condition) provided to Owl_ode_base.Ode.odeint. For example Owl.Mat.mat.

type f

f is type of the evolution function. For example, in the case of sympletic solvers, type state = Owl.Mat.(mat*mat) and type f = state -> float -> Owl.Mat.mat.

type step_output

step_output defines the type of the output of Owl_ode.Ode.step. For example, in the case of native adaptive solvers, type output = Owl.Mat.(mat * float * float * bool), corresponds to matrices and floats that contain respectively the y1, t1, dt, and whether this step was valid

type solve_output

solve_output defines the type of the output of Owl_ode.Ode.odeint. For example, in the case of sympletc solvers, type output = Owl.Mat.(mat * mat * mat), corresponds to matrices that contain respectively the time, position, and momentum coordinates of the integrated solution

val step : f -> dt:float -> state -> float -> step_output

step f dt y0 t0 () solves for one step given dt, y0, t0 and the evolution function. Several such functions have already been implemented in this library and can be used as reference.

val solve : f -> state -> tspec -> unit -> solve_output

solve f y0 tspec () solves the initial value problem

∂ₜ y = f(y, t) y(t₀) = y₀

with the given evolution function f, initial condition y0, and temporal specification tspec, and returns the desired outputs of type output. Several such functions have already been implemented in this library and can be used as reference.