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A fully Galerkin method for the damped generalized regularized long‐wave (DGRLW) equation
Author(s) -
Achouri Talha,
Ayadi Mekki,
Omrani Khaled
Publication year - 2009
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.20367
Subject(s) - mathematics , extrapolation , galerkin method , convergence (economics) , a priori and a posteriori , partial differential equation , nonlinear system , scheme (mathematics) , partial derivative , crank–nicolson method , mathematical analysis , physics , philosophy , epistemology , quantum mechanics , economics , economic growth
In this article, a fully discrete Galerkin scheme based on a nonlinear Crank–Nicolson method to approximate the solution of the DGRLW equation is constructed. Some a priori bounds are proved as well as error estimates. Then, a linearized modification scheme by an extrapolation method is discussed. The two schemes are time second order convergence. The last part is devoted to some numerical results. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009