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HAIT Journal of Science and Engineering C Volume 4, Issues 1-2, pp. 128-135 © 2007 Holon Institute of Technology | ||||
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On complex-stepped Runge-Kutta methods for exact time integration of linear PDEs
Denis M. Filatov
Centre for Atmospheric Science (CCA), UNAM, | Circuito Exterior, C.P. 04510, Mexico email: denisfilatov@mail.ru Received 12 October 2004, accepted 30 April 2006
| We extend the approaches developed in the papers by Kaps and Rentrop [Numerische Mathematik 33, (1979)] and by Schatzman [J. Sci. Comput. 17, (2002)], and suggest a method for highly accurate time integration of linear first-order evolutionary PDEs. The main idea is to generalise the Runge-Kutta methods for complex timesteps, which reduces the problem of accurate integration to the search for an optimal temporal path on the complex plane. Theoretically the method admits exact integration with finite timesteps. Keywords: Runge-Kutta methods, linear partial differential equations, time integration, conservative finite difference schemes, complex plane.
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