Two-step numerical methods for parabolic differential equations

A family of two-stepA-stable methods of maximal order for the numerical solution of ordinary differential systems is developed. If these methods are applied to the stiff, large systems which originate from linear parabolic differential equations they yield a large, sparse set of linear algebraic equations of special form. This set is considerably easier to solve than the algebraic equations which are obtained when using diagonal Obrechkoff methods, which are one-step,A-stable and of maximal order