BVP Problems

Defines an BVP problem. Documentation Page: https://docs.sciml.ai/DiffEqDocs/stable/types/bvp_types/

Mathematical Specification of a BVP Problem

To define a BVP Problem, you simply need to give the function and the initial condition which define an ODE:

along with an implicit function bc! which defines the residual equation, where

is the manifold on which the solution must live. A common form for this is the two-point BVProblem where the manifold defines the solution at two points:

Problem Type

Constructors

or if we have an initial guess function initialGuess(t) for the given BVP, we can pass the initial guess to the problem constructors:

For any BVP problem type, bc! is the inplace function:

where residual computed from the current u. u is an array of solution values where u[i] is at time t[i], while p are the parameters. For a TwoPointBVProblem, t = tspan. For the more general BVProblem, u can be all of the internal time points, and for shooting type methods u=sol the ODE solution. Note that all features of the ODESolution are present in this form. In both cases, the size of the residual matches the size of the initial condition.

Parameters are optional, and if not given, then a NullParameters() singleton will be used which will throw nice errors if you try to index non-existent parameters. Any extra keyword arguments are passed on to the solvers. For example, if you set a callback in the problem, then that callback will be added in every solve call.

Fields