Evaluating the Evans function: Order reduction in numerical methods

We consider the numerical evaluation of the Evans function, a Wronskian-like determinant that arises in the study of the stability of travelling waves. Constructing the Evans function involves matching the solutions of a linear ordinary differential equation depending on the spectral parameter. The problem becomes stiff as the spectral parameter grows. Consequently, the Gauss–Legendre method ha...

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Numerical evaluation of the Evans function by Magnus integration

We use Magnus methods to compute the Evans function for spectral problems as arise when determining the linear stability of travelling wave solutions to reactiondiffusion and related partial differential equations. In a typical application scenario, we need to repeatedly sample the solution to a system of linear non-autonomous ordinary differential equations for different values of one or more ...

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ar X iv : m at h / 06 05 58 1 v 2 [ m at h . N A ] 2 8 N ov 2 00 6 EVALUATING THE EVANS FUNCTION : ORDER REDUCTION IN NUMERICAL METHODS

We consider the numerical evaluation of the Evans function, a Wronskian-like determinant that arises in the study of the stability of travelling waves. Constructing the Evans function involves matching the solutions of a linear ordinary differential equation depending on the spectral parameter. The problem becomes stiff as the spectral parameter grows. Consequently, the Gauss–Legendre method ha...

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ar X iv : m at h / 06 05 58 1 v 1 [ m at h . N A ] 2 2 M ay 2 00 6 EVALUATING THE EVANS FUNCTION : ORDER REDUCTION IN NUMERICAL METHODS

We consider the numerical evaluation of the Evans function, a Wronskian-like determinant that arises in the study of the stability of travelling waves. Constructing the Evans function involves matching the solutions of a linear ordinary differential equation depending on the spectral parameter. The problem becomes stiff as the spectral parameter grows. Consequently, the Gauss–Legendre method ha...

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ar X iv : m at h . N A / 0 60 55 81 v 1 2 2 M ay 2 00 6 EVALUATING THE EVANS FUNCTION : ORDER REDUCTION IN NUMERICAL METHODS

We consider the numerical evaluation of the Evans function, a Wronskian-like determinant that arises in the study of the stability of travelling waves. Constructing the Evans function involves matching the solutions of a linear ordinary differential equation depending on the spectral parameter. The problem becomes stiff as the spectral parameter grows. Consequently, the Gauss–Legendre method ha...

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Evaluating the Evans function: Order reduction in numerical methods

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