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The authors present a new singular function boundary integral method for the numerical solution of problems with singularities which is based on approximation of the solution by the leading terms of… (More)

- Georgios Akrivis, D. T. Papageorgiou, Yiorgos Sokratis Smyrlis
- SIAM J. Scientific Computing
- 2012

We analyze and implement fully discrete schemes for periodic initial value problems for a general class of dispersively modified Kuramoto-Sivashinsky equations. Time discretizations are constructed… (More)

- Yiorgos Sokratis Smyrlis, D. T. Papageorgiou
- Proceedings of the National Academy of Sciences…
- 1991

The results of extensive computations are presented to accurately characterize transitions to chaos for the Kuramoto-Sivashinsky equation. In particular we follow the oscillatory dynamics in a window… (More)

We present the results of extensive numerical experiments of the spatially periodic initial value problem for the Kuramoto-Sivashinsky equation. Our concern is with the asymptotic nonlinear dynamics… (More)

We report the results of extensive numerical experiments on the Kuramoto-Sivashinsky equation in the strongly chaotic regime as the viscosity parameter is decreased and increasingly more linearly… (More)

- Yiorgos Sokratis Smyrlis
- Math. Comput.
- 2009

In the present work, we investigate the applicability of the method of fundamental solutions for the solution of boundary value problems of elliptic partial differential equations and elliptic… (More)

- Yiorgos Sokratis Smyrlis
- Numerische Mathematik
- 2009

The method of fundamental solutions (MFS) is a Trefftz–type technique in which the solution of an elliptic boundary value problem is approximated by a linear combination of translates of fundamental… (More)

- Yiorgos Sokratis Smyrlis, Andreas Karageorghis
- J. Sci. Comput.
- 2001

The Method of Fundamental Solutions (MFS) is a boundary-type method for the solution of certain elliptic boundary value problems. The basic ideas of the MFS were introduced by Kupradze and Alexidze… (More)

In this paper the nonlinear stability of two-phase core-annular flow in a pipe is examined when the acting pressure gradient is modulated by time harmonic oscillations and viscosity stratification… (More)

- Yiorgos Sokratis Smyrlis, Andreas Karageorghis
- Numerical Algorithms
- 2004

The Method of Fundamental Solutions (MFS) is a boundary-type meshless method for the solution of certain elliptic boundary value problems. In this work, we propose an efficient algorithm for the… (More)