Modified Bateman solution for identical eigenvalues

In this paper we develop a general solution to the Bateman equations taking into account the special case of identical eigenvalues. A characteristic of this new solution is the presence of higher order derivatives. It is shown that the derivatives can be obtained analytically and also computed in an efficient manner.

► Solving indeterminacies due to identical eigenvalues in Bateman’s solution.
► Exact analytical solution of Bateman’s equations for identical eigenvalues.
► Algorithm calculating higher order derivatives appearing in this solution.
► Alternative evaluation of the derivatives through the Taylor polynomial.
► Implementation of an example program demonstrating the developed solution.