BVP Solvers

Recomended Methods

GeneralMIRK4 is a good well-rounded method when the problem is not too large. It uses highly stable trust region methods to solve a 4th order fully implicit Runge-Kutta scheme. As an alternative on general BVProblems, the Shooting method paired with an appropriate integrator for the IVP, such as Shooting(Tsit5()), is a flexible and efficient option. This will allow one to combine callbacks/event handling with the BVP solver, and the high order interpolations can be used to define complex boundary conditions. However, Shooting methods can in some cases be prone to sensitivity of the boundary condition.

When the problem is a large two-point boundary value problem that is sensitive to the boundary conditions, MIRK4 utilizes a sparse Jacobian to greatly improve the efficiency.

Full List of Methods

BoundaryValueDiffEq.jl

• Shooting - A wrapper over initial value problem solvers.
• GeneralMIRK4 - A 4th order collocation method using an implicit Runge-Kutta tableau solved using a trust region dogleg method from NLsolve.jl.
• MIRK4 - A 4th order collocation method using an implicit Runge-Kutta tableau with a sparse Jacobian. Compatible only with two-point boundary value problems.