A Legendre-pseudospectral method for computing travelling waves with corners (slope discontinuities) in one space dimension with application to Whitham's equation family
The author proposes a Legendre-pseudospectral method for computing travelling waves with corners in one space dimension with application to Whitham's equation family. Because ``corner'' waves are not smooth, standard numerical methods converge poorly as the number of grid points is increased. He devises a Legendre-pseudospectral method which is uncorrupted by the singularity. A key step is to derive an extra boundary condition which uniquely identified the corner wave. Although his method is illustrated by the so-called ``Whitham's equation'', the ideas are widely applicable.
scientific article; zbMATH DE number 1965156
scientific article