Orthogonal Collocation For Hyperbolic PDEs And Computation Of Invariant Tori

Mathematics Research Report MRR95-060

Orthogonal Collocation For Hyperbolic PDEs And Computation Of Invariant Tori

K.D. Edoh, R.D. Russell and W. Sun

Abstract: A partial differential equation approach has been used recently in various contexts for computing invariant tori for systems of ordinary differential equations. We present an O(h⁴) collocation method for solving these resulting nonlinear hyperbolic partial differential equations with periodic boundary conditions. A convergence analysis is given and numerical results for the method are contrasted with those of some previously tested methods. We also introduce an adaptive grid refinement scheme and use it to study the torus breakdown.

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