Solving Boundary Value Problems in R

Boundary Value Problems can be solved in R using shooting, MIRK and collocation methods and these can be found in the R package bvpSolve. The functions in this R package have an interface which is similar to the interface of the initial value problem solvers in the package deSolve. The default input to the solvers is very simple, requiring specification of only one function that calculates the derivatives while the boundary conditions are represented as simple vectors. However, in order to speed-up the simulations, and to increase the number of problems that can be solved, it is also possible to specify the boundary conditions by means of a function and provide analytic functions for the derivative and boundary gradients. In this chapter we demonstrate how to solve BVPs using a variety of well-known test problems, illustrating a wide range of difficulties in solving BVPs. We show how to use (manual and automatic) continuation, how difficult boundary conditions can be handled, and give many examples of how to convert BVPs to standard form. Some BVPs are much better solved using the finite difference methods as explained in the PDE chapter. We give an example of such a boundary value problem at the end of this chapter.