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UBC CS TR-84-13 Summary

Stability of Collocation at Gaussian Points, October 1984 Uri Ascher and G. Bader

Symmetric Runge-Kutta schemes are particularly useful for solving stiff two-point boundary value problems. Such A-stable schemes perform well in many cases, but it is demonstrated that in some instances the stronger property of algebraic stability is required.

A characterization of symmetric, algebraically stable Runge-Kutta schemes is given. The class of schemes thus defined turns out not to be very rich: The only collocation schemes in it are those based on Gauss points, and other schemes in the class do not seem to offer any advantage over collocation at Gaussian points.


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