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Numerical solution of a coupled Korteweg–de Vries equations by collocation method
Author(s) -
Ismail M.S.
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.20343
Subject(s) - mathematics , korteweg–de vries equation , quintic function , partial differential equation , collocation method , orthogonal collocation , collocation (remote sensing) , partial derivative , stability (learning theory) , soliton , mathematical analysis , scheme (mathematics) , differential equation , nonlinear system , physics , ordinary differential equation , computer science , quantum mechanics , machine learning
A numerical method for solving the coupled Korteweg‐de Vries (CKdV) equation based on the collocation method with quintic B‐spline finite elements is set up to simulate the solution of CKdV equation. Invariants and error norms are studied wherever possible to determine the conservation properties of the algorithm. Simulation of single soliton, interaction of two solitons, and birth of solitons are presented. A linear stability analysis shows the scheme to be unconditionally stable. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009