High order variable mesh off-step discretization for the solution of 1-D non-linear hyperbolic equation

Swarn Singh (Lead / Corresponding author), Ping Lin (Lead / Corresponding author)

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)

    Abstract

    In this paper, we propose a new high order three-level implicit method based on off-step discretization on a non-uniform mesh for the solution of 1-D 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. Our method is directly applicable to the wave equation in polar coordinates and we do not require any special technique to handle singular coefficients of the differential equation. The method is convergent for uniform mesh. Numerical results are provided to justify the usefulness of the proposed method.
    Original languageEnglish
    Pages (from-to)629-638
    Number of pages10
    JournalApplied Mathematics and Computation
    Volume230
    DOIs
    Publication statusPublished - 1 Mar 2014

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