Hermite interpolation and A-stable methods for stiff ordinary differential equations

Hermite interpolation in the form of Newton's divided difference expressions is employed to give a generating function for A-stable difference methods of order 2n. These methods can be used to solve the initial value ordinary differential equation y′=g(y,t), y(a)=η. The extension to higher dimensions is considered, and practical suggestions are given for step size changes and order changes.