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Gegenbauer wavelet collocation method for the extended Fisher‐Kolmogorov equation in two dimensions
Author(s) -
Çelik İbrahim
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6300
Subject(s) - mathematics , mathematical analysis , partial differential equation , wavelet , dimension (graph theory) , collocation (remote sensing) , differential equation , nonlinear system , pure mathematics , physics , remote sensing , quantum mechanics , artificial intelligence , computer science , geology
Gegenbauer wavelets operational matrices play an important role in the numeric solution of differential equations. In this study, operational matrices of r th integration of Gegenbauer wavelets are derived and used to obtain an approximate solution of the nonlinear extended Fisher‐Kolmogorov (EFK) equation in two‐space dimension. Nonlinear EFK equation is converted into the linear partial differential equation by quasilinearization technique. Numerical examples have shown that present method is convergent even in the case of a small number of grid points. The results of the presented method are in a good agreement with the results in literature.