Solving Heterogeneous Differential Equations Using Green Function

Abstract

This study dealt with a group of theories that can be applied in solving functional differential equations. These theories were developed during a quarter of a century by a large group of mathematicians called Perm Seminar. The results of the seminar were published in scientific journals ((boundary value problems)) and ((Functional Differential Equations)) issued in 1976 -1992 by Perm Polytechnic Institute. We tackled in this chapter an introduction to functional differential equations and the concept of Banach Space. That is because all theories about functional differential equations were based on Banach Space and also Green operator as an integral operator. We also mentioned Green’s Matrix and its relationship with Green operator in solving differential equations systems and the concepts of Eigenvalues and Eigenvectors using the characteristic values in solving the differential equation systems. We also tackled in the third chapter differential equations in scalar function space with continuous derivation of order (n-1) and the concept of Green equations in solving differential equation of the second order and solving initial value problems for heterogeneous differential equations using Green functions.