BVP Solvers

The MIRK methods are recommended in most scenarios given their improved stability properties over the other methods. They have adaptivty and sparsity handling which allows for them to handle large-scale and difficult problems. However, they are not compatible with callbacks / event handling (i.e. discontinuities), and in such cases Shooting is required, where Shooting should be used with an appropriate ODE solver such as Shooting(Tsit5()) or Shooting(FBDF()). Additionally, in many cases Shooting may be faster if it converges, though it is a lot less numerically robust.

Full List of Methods

BoundaryValueDiffEq.jl

Shooting Methods

  • Shooting - A wrapper over initial value problem solvers, it reduces bvp to an initial value problem and solves the ivp.

MIRK Collocation Methods

All MIRK methods have defect control adaptivity by default which adapts the mesh (dt) automatically. This can be turned off via the keyword argument adaptive = false.

  • MIRK2 - A 2nd order collocation method using an implicit Runge-Kutta tableau with a sparse Jacobian.
  • MIRK3 - A 3rd order collocation method using an implicit Runge-Kutta tableau with a sparse Jacobian.
  • MIRK4 - A 4th order collocation method using an implicit Runge-Kutta tableau with a sparse Jacobian.
  • MIRK5 - A 5th order collocation method using an implicit Runge-Kutta tableau with a sparse Jacobian.
  • MIRK6 - A 6th order collocation method using an implicit Runge-Kutta tableau with a sparse Jacobian.