Direct Integration of Systems of Linear Differential and Difference Equations

Abstract

Traditionally the Euler method is used for solving systems of linear
differential equations. The method is based on the use of eigenvalues
of a system's coefficients matrix. Another method to solve those systems
is the D'Alembert integrable combination method.
In this paper, we present a new method for solving systems of linear
differential and difference equations. The main idea of the method
is using the coefficients matrix eigenvalues to find integrable
combinations of system variables. This method is particularly
advantageous when nonhomogeneous systems are considered.