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Two‐level linearized and local uncoupled difference schemes for the two‐component evolutionary Korteweg‐de Vries system
Author(s) -
Shen JinYe,
Sun ZhiZhong
Publication year - 2020
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.22385
Subject(s) - mathematics , norm (philosophy) , component (thermodynamics) , convergence (economics) , korteweg–de vries equation , space (punctuation) , order (exchange) , mathematical analysis , nonlinear system , physics , quantum mechanics , thermodynamics , linguistics , philosophy , finance , political science , law , economics , economic growth
The two‐level linearized and local uncoupled spatial second order and compact difference schemes are derived for the two‐component evolutionary system of nonhomogeneous Korteweg‐de Vries equations. It is shown by the mathematical induction that these two schemes are uniquely solvable and convergent in a discrete L ∞ norm with the convergence order of O( τ 2 + h 2 ) and O( τ 2 + h 4 ), respectively, where τ and h are the step sizes in time and space. Three numerical examples are given to confirm the theoretical results.