Abstract
Abstract A new universal solver is proposed for general hyperbolic equations; multi-dimensional, linear and nonlinear equations with dissipative and dispersive terms. The scheme uses piecewise cubic polynomial interpolation inside meshes. The physical quantity and its spatial derivative are advanced in time according to the given equation. The scheme not only describes a sharp discontinuity with only one mesh but also reproduces the traveling wave train in the dispersive media. The extension to higher dimensions is straightforward.
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