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A high-order Dirac-delta regularization with optimal scaling in the spectral solution of one-dimensional singular hyperbolic conservation laws. (English) Zbl 1308.65173

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
35Q53 KdV equations (Korteweg-de Vries equations)
76N15 Gas dynamics (general theory)
35M12 Boundary value problems for PDEs of mixed type
76M22 Spectral methods applied to problems in fluid mechanics
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