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An analysis for a high‐order difference scheme for numerical solution to u tt = A ( x, t ) u xx + F ( x, t, u, u t , u x )
Author(s) -
Li WeiDong,
Sun ZhiZhong,
Zhao Lei
Publication year - 2007
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.20194
Subject(s) - mathematics , uniqueness , norm (philosophy) , dirichlet boundary condition , mathematical analysis , order (exchange) , convergence (economics) , nonlinear system , boundary value problem , law , physics , finance , quantum mechanics , political science , economics , economic growth
This article is concerned with a high‐order implicit difference scheme presented by Mohanty, Jain, and George for the nonlinear hyperbolic equation u tt = A ( x , t ) u xx + F ( x , t , u , u t , u x ) with Dirichlet boundary conditions. Some prior estimates of the difference solution are obtained by the energy methods. The solvability of the difference scheme is proved by the energy method and Brower's fixed point theorem. Similarly, the uniqueness, the convergence in L ∞ ‐norm and the stability of the difference solution are obtained. A numerical example is provided to demonstrate the validity of the theoretical results. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 484–498, 2007