Note on filon-type integration for higher order exponential time differencing methods in stiff systems

Shu-huang Xiang

doi:10.1007/s11771-005-0417-y

Journal of Central South University ›› 2005, Vol. 12 ›› Issue (Suppl 1) : 298 -303. DOI: 10.1007/s11771-005-0417-y

Mathematics

Note on filon-type integration for higher order exponential time differencing methods in stiff systems

Shu-huang Xiang ¹^,^a

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Abstract

The Filon-type quadrature is efficient for highly oscillatory functions — Fourier transforms. Based on Cox and Matthews’ ETD schemes, the higher order single step exponential time differencing schemes are presented based on the Filon-type integration and the A-stability of the two-order Adams-Bashforth exponential time differencing scheme is considered. The effectiveness and accuracy of the schemes is tested.

Keywords

exponential time differencing method / stiff system / Filon method / Runge-Kutta method

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Shu-huang Xiang. Note on filon-type integration for higher order exponential time differencing methods in stiff systems. Journal of Central South University, 2005, 12(Suppl 1): 298-303 DOI:10.1007/s11771-005-0417-y