On functionally-fitted Runge-Kutta methods

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On functionally-fitted Runge-Kutta methods

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Title: On functionally-fitted Runge-Kutta methods
Author: N.S., Hoang; Sidje, R.B.; N.H., Cong
Abstract: Functionally-fitted methods are generalizations of collocation techniques to integrate an equation exactly if its solution is a linear combination of a chosen set of basis functions. When these basis functions are chosen as the power functions, we recover classical algebraic collocation methods. This paper shows that functionally-fitted methods can be derived with less restrictive conditions than previously stated in the literature, and that other related results can be derived in a much more elegant way. The novelty in our approach is to fully retain the collocation framework without reverting back into derivations based on cumbersome Taylor series expansions. ?? Springer Science + Business Media B.V. 2006.
URI: http://tainguyenso.vnu.edu.vn/jspui/handle/123456789/7222
Date: 2006

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