Direct algebraic solution for linear differential equations using PL transform

A new direct algebraic algorithm is developed for the numerical solution of linear differential equations. The differential equations are solved via PL transform by means of an integral operator without iterative calculations. The use of PL transform paves the way, with the aid of symbolic and algebraic manipulation system such as REDUCE for instance, for a simple direct solution for boundary value problems as well as initial value problems of linear differential equations. Examples show that the accuracy of solution is excellent considering the limited length of the PL transform that is used.