High Order Variable Mesh Approximation for the Solution of 1D Non-linear Hyperbolic Equation
نویسندگان
چکیده
In this paper, we propose a new high order Numerov type three-level implicit compact discretization on a non-uniform mesh for the solution of one-space dimensional non-linear hyperbolic partial differential equation of the form utt = uxx + g(x, t, u, ux, ut) subject to appropriate initial and Dirichlet boundary conditions. We use only three evaluations of the function g and three grid points at each time level in a compact cell. We also discuss how our method is able to handle the wave equation in polar coordinates. Numerical results are provided to justify the usefulness of the proposed method.
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