A numerical method for one‐dimensional nonlinear Sine‐Gordon equation using collocation and radial basis functions | Zendy

Dehghan M. | Zendy; Shokri Ali | Zendy

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A numerical method for one‐dimensional nonlinear Sine‐Gordon equation using collocation and radial basis functions

Author(s) -

Dehghan M.,

Shokri Ali

Publication year - 2008

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.20289

Subject(s) - radial basis function , mathematics , collocation (remote sensing) , sine , collocation method , partial differential equation , nonlinear system , orthogonal collocation , mathematical analysis , sine gordon equation , partial derivative , basis (linear algebra) , basis function , scheme (mathematics) , differential equation , geometry , ordinary differential equation , artificial neural network , computer science , physics , soliton , quantum mechanics , machine learning

In this article, we propose a numerical scheme to solve the one‐dimensional undamped Sine‐Gordon equation using collocation points and approximating the solution using Thin Plate Splines (TPS) radial basis function (RBF). The scheme works in a similar fashion as finite difference methods. The results of numerical experiments are presented and are compared with analytical solutions to confirm the good accuracy of the presented scheme.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008

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