A structured matrix problem in dynamical systems

This paper considers the iterative solution of a class of nonsymmetric linear systems where the coefficient matrices have a very specific block structure. These arise in the context of dynamical systems when computing a smooth invariant manifold for the forced van der Pol oscillator. A pseudo-spectral approximation method is described to explain the origin of the matrix structure and efficient solution of the linear equations is discussed. The convergence behaviour of three widely used nonsymmetric iterative methods is illustrated using numerical experiments.