Explicit Implementation of Collocation Methods for Stiff Systems with Complex Spectrum

B. V. Faleichik2
Computational Mathematics Department,
Faculty of Applied Mathematics and Computer Science,
Belarusian State University,
220030 Minsk, Belarus
Received October 21, 2009; accepted in revised form January 19, 2010.
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.

c 2010 European Society of Computational Methods in Sciences and Engineering
Keywords: Stiff problems, explicit methods, collocation methods, iterated Runge-Kutta
methods, linear analysis of convergence.
Mathematics Subject Classification: 65L05, 65L06, 65L20

 

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