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Solitary wave solutions of the MRLW equation using radial basis functions
Author(s) -
Dereli Yilmaz
Publication year - 2012
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.20616
Subject(s) - radial basis function , mathematics , collocation (remote sensing) , regularized meshless method , basis (linear algebra) , mathematical analysis , partial differential equation , collocation method , wave equation , invariant (physics) , basis function , motion (physics) , differential equation , classical mechanics , physics , geometry , singular boundary method , finite element method , ordinary differential equation , mathematical physics , computer science , machine learning , boundary element method , artificial neural network , thermodynamics
In this study, traveling wave solutions of the modified regularized long wave (MRLW) equation are simulated by using the meshless method based on collocation with well‐known radial basis functions. The method is tested for three test problems which are single solitary wave motion, interaction of two solitary waves and interaction of three solitary waves. Invariant values for all test problems are calculated, also L 2 , L ∞ norms and values of the absolute error for single solitary wave motion are calculated. Numerical results by using the meshless method with different radial basis functions are presented. Figures of wave motions for all test problems are shown. Altogether, meshless methods with radial basis functions solve the MRLW equation very satisfactorily.© 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 235–247, 2012