Explicit Implementation of Collocation Methods for Stiff Systems with Complex Spectrum

Abstract

Currently there are two general ways to solve stiff differential equations numerically. The first approach is based on implicit methods and the second uses explicit stabilized Runge–Kutta methods, also known as Chebyshev methods. Implicit methods are great for very stiff problems of not very large dimension, while stabilized explicit methods are efficient for very big systems of not very large stiffness and real spectrum. In this paper we describe methods which are explicit and are capable of solving stiff systems with complex eigenvalues of Jacobi matrix.