A lifting method for hyperbolic equations with δ-singularities

Abstract

Abstract In this paper, we propose a method to lift the solution space of hyperbolic equations with δ-singularities such that dealing with the annoying δ-singularities directly is avoided. Thus, the easily implemented finite difference schemes can be employed conveniently for solving such problems with δ-singularities. In particular, we consider a fifth-order nonlinear finite difference scheme that can capture discontinuities robustly. To demonstrate the effectiveness of the proposed method, numerical examples are presented. Additionally, a novel splitting method is also proposed to extend the lifting method to high dimensions.