THE IMPROVEMENT OF ODE SOLVER METHOD IN THE ANALYSIS OF ODE EIGENVALUE PROBLEM

An integrated algorithm of solving ODE eigenvalue problems was proposed before. A program code called COLEGN for solving this kind of problem was also developed based on this method, but the code requires the user to input both the equivalent nonlinear ODE system and the linear ODE system and hence is not easy to use. The essential relations between these two ODE systems are studied in this paper. It is found that the linear ODE system can be obtained completely from the nonlinear ODE system. The formulation to extract the linear ODE system is proposed in this paper and incorporated into COLEGN. The new COLEGN only needs the user to input the nonlinear ODE system and is easier to use. In addition, the case that the eigenvalue appears in the boundary conditions is also treated in this paper, which expands the algorithms applicability.