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Numerical study of a conservative weighted compact difference scheme for the symmetric regularized long wave equations
Author(s) -
Li Shuguang
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22285
Subject(s) - mathematics , tridiagonal matrix , scheme (mathematics) , convergence (economics) , algebraic equation , norm (philosophy) , numerical analysis , mathematical analysis , algebraic number , compact finite difference , numerical stability , computation , stability (learning theory) , tridiagonal matrix algorithm , algorithm , nonlinear system , eigenvalues and eigenvectors , physics , quantum mechanics , machine learning , political science , computer science , law , economics , economic growth
In this article, a new weighted and compact conservative difference scheme for the symmetric regularized long wave (SRLW) equations is considered. The new scheme is decoupled and linearized in practical computation, that is, at each time step only two tridiagonal systems of linear algebraic equations need to be solved. It is proved by the discrete energy method that the compact scheme is uniquely solvable, the convergence and stability of the difference scheme are obtained, and its numerical convergence order is O ( τ 2 + h 4 ) in theL ∞ ‐norm. Numerical experiment results show that the scheme is efficient and reliable.