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Finite difference discretization of the Benjamin‐Bona‐Mahony‐Burgers equation
Author(s) -
Omrani Khaled,
Ayadi Mekki
Publication year - 2008
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.20256
Subject(s) - mathematics , burgers' equation , discretization , partial differential equation , norm (philosophy) , uniqueness , mathematical analysis , finite difference method , convergence (economics) , finite difference , finite difference coefficient , dimension (graph theory) , finite element method , pure mathematics , mixed finite element method , law , physics , political science , economics , thermodynamics , economic growth
Abstract Numerical solutions of the Benjamin‐Bona‐Mahony‐Burgers equation in one space dimension are considered using Crank‐Nicolson‐type finite difference method. Existence of solutions is shown by using the Brower's fixed point theorem. The stability and uniqueness of the corresponding methods are proved by the means of the discrete energy method. The convergence in L ∞ ‐norm of the difference solution is obtained. A conservative difference scheme is presented for the Benjamin‐Bona‐Mahony equation. Some numerical experiments have been conducted in order to validate the theoretical results.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007