Hermite cubic spline collocation methods with upwind features

Weiwei Sun


In this paper, we present an eigenvalue analysis of the first-order Hermite cubic spline collocation differentiation matrices with arbitrary collocation points. Some important features are explored and the method is compared with some other discrete methods, such as finite difference methods. A class of spline collocation methods with upwind features is proposed for solving singular perturbation problems.

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DOI: http://dx.doi.org/10.21914/anziamj.v42i0.650

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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.