A MOVING MESH METHOD FOR
THE NONLINEAR SHRÖDINGER EQUATION
Abstract. In this paper we apply a moving mesh method to a numerically challenging problem namely, the nonlinear Schrödinger (NLS) equation. This problem arises from applications where it has been used to describe the motion of a vortex filament in incompressible fluids and also to model fractal fibre architecture of aortic heart valve lea ets in the study of the human heart. Our aims are to show the existence and the properties of the numerical solution of a nonlinear shrödinger's equation. This method is used to investigate with highly resolved numerics the solution's behavior for small dispersion parameters. Numerical simulations has shown that this scheme is very efficient to solve this problem.
AMS Subject Classification: 65L12, 65M20, 65N40, 65M50


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DOI: 10.12732/ijam.v29i1.9

Volume: 29
Issue: 1
Year: 2016