Gegenbauer wavelet collocation method for the extended Fisher‐Kolmogorov equation in two dimensions
İbrahim Çelik
Abstract
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.
Topics & Concepts
MathematicsMathematical analysisPartial differential equationWaveletDimension (graph theory)Collocation (remote sensing)Differential equationNonlinear systemApplied mathematicsPure mathematicsArtificial intelligenceQuantum mechanicsPhysicsGeologyComputer scienceRemote sensingFractional Differential Equations SolutionsModel Reduction and Neural NetworksDifferential Equations and Numerical Methods