Stability of Collocation at Gaussian Points
Authors:
- U. AscherUAU. Ascher
- G. BaderGBG. Bader
- 1 April 1986
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 23 (2) , 412-422
Abstract
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.Keywords
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