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New conservative difference schemes with fourth‐order accuracy for some model equation for nonlinear dispersive waves
Author(s) -
Ghiloufi Ahlem,
Omrani Khaled
Publication year - 2018
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.22208
Subject(s) - mathematics , uniqueness , convergence (economics) , korteweg–de vries equation , norm (philosophy) , nonlinear system , stability (learning theory) , mathematical analysis , dispersive partial differential equation , a priori and a posteriori , finite difference , partial differential equation , philosophy , physics , epistemology , quantum mechanics , machine learning , political science , computer science , law , economics , economic growth
In this article, some high‐order accurate difference schemes of dispersive shallow water waves with Rosenau‐KdV‐RLW‐equation are presented. The corresponding conservative quantities are discussed. Existence of the numerical solution has been shown. A priori estimates, convergence, uniqueness, and stability of the difference schemes are proved. The convergence order is O ( h 4 + k 2 ) in the uniform norm without any restrictions on the mesh sizes. At last numerical results are given to support the theoretical analysis.