Solutions of the generalized Langevin equation by a method of recurrence relations

The generalized Langevin equation is solved by a method alternative to one due to Mori. We deduce certain recurrence relations which are used to obtain formal solutions for the relaxation function, the random forces. In certain cases, our formalism is capable of providing solutions directly from the forms of the recurrence relations. This capability is demonstrated through the currently important two-dimensional electronic systems and also the spin van der Waals model.