Efficient fourth order P-stable formulae (Q1095612)

The author considers a family of fourth order P-stable methods applied to the initial value problem of a nonlinear second order differential system; they give rise to a nonlinear algebraic system at each step which is solvable by a modified Newton method. He derives methods which require only two (new) function evaluations per iteration and for which the iteration matrix is a true real perfect square. Computation problems are discussed, comparation with seven numerical methods are included, and many other methods mentioned.