sine-Gordon solver for FreeFem++

This script allows to solve numerically the sine-Gordon equation in a Y-junction geometry using the Finite Element Method (FEM). The scheme is of 2nd order in space and time. The implixit-explicit time stepping method is of the Crank-Nicolson type and it possesses excellent energy conservation properties.

Some scientific results on the sine-Gordon equation in a tree-like geometry were obtained using this method. They are briefly described in the following preprint:

• J.-G. Caputo & D. Dutykh. Nonlinear waves in networks: a simple approach using the sine-Gordon equation. Submitted, 2014

Any comments are welcome!

Authors

• Denys Dutykh (CNRS - LAMA, University of Savoie)
• Jean-Guy Caputo (LMI - INSA de Rouen)

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FreeFem++

The code FreeFem++ is a Partial Differential Equation (PDE) solver based on the Finite Element Method (FEM) which can be freely downloaded for various platforms here:

• http://www.freefem.org/ff++/