On the derivation of high order symmetric MIRK formulae with interpolants for solving two-point boundary value problems (Q2708030)

This paper deals with iterated deferred correction methods for the numerical solution of first-order systems of nonlinear two-point boundary value problems of the form NEWLINE\[NEWLINE{dy\over dx}= f(x,y),\quad a< x< b,\quad g(y(a), y(b))= 0\tag{1}NEWLINE\]NEWLINE without an assumption that only a unique solution of (1) exists. One of these methods is a mono-implicit Runge-Kutta (MIRK) formulae. The author shows how an eight-order interpolant can be derived in a reasonably efficient way. The quality of interpolants is demonstrated by seven layer problems with only linear boundary conditions.