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Lie-symmetry based integrators are constructed in order to preserve the local invariance properties of the equations. The geometrical methods leading to discretized equations for numerical computations involve many different concepts. Therefore they give rise to numerical schemes that vary in the accuracy, in the computational cost and in the(More)
Geometric discretizations that preserve certain Hamiltonian structures at the discrete level has been proven to enhance the accuracy of numerical schemes. In particular, numerous symplectic and multi-symplectic schemes have been proposed to solve numerically the celebrated Korteweg-de Vries (KdV) equation. In this work, we show that geometrical schemes are(More)
In this study, we discuss an approximate set of equations describing water wave propagating in deep water. These generalized Klein–Gordon (gKG) equations possess a variational formulation, as well as a canonical Hamiltonian and multi-symplectic structures. Periodic travelling wave solutions are constructed numerically to high accuracy and compared to a(More)
Invariant numerical schemes possess properties that may overcome the numerical properties of most of classical schemes. When they are constructed with moving frames, invariant schemes can present more stability and accuracy. The cornerstone is to select relevant moving frames. We present a new algorithmic process to do this. The construction of invariant(More)
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