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The meshless kernel-based method of lines for solving the equal width equation. (English) Zbl 1282.76086

Summary: The Equal Width equation governs nonlinear wave phenomena like waves in shallow water. Here, it is solved numerically by the Method of Lines using a somewhat unusual setup. There is no linearization of the nonlinear terms, no error in handling the starting approximation, and there are boundary conditions only at infinity. To achieve a space discretization of high accuracy with only few trial functions, meshless translates of radial kernels are used. In the numerical examples, the motion of solitary waves, the interaction of two and three solitary waves, the generation of wave undulation, the Maxwell initial condition, and the clash of two colliding solitary waves are simulated. Our numerical results compare favourably with results of earlier papers using other techniques.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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