Application of a numerical method using radial basis functions to nonlinear partial differential equations

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Küçük Resim

Tarih

2011

Dergi Başlığı

Dergi ISSN

Cilt Başlığı

Yayıncı

Selcuk University Research Center of Applied Mathematics

Erişim Hakkı

info:eu-repo/semantics/openAccess

Özet

In this paper, we propose a meshfree method for numerical solution of various classes of partial differential equations (PDEs), such as the Boussinesq system, Drinefel'd-Sokolov-Wilson equations, and Hirota-Satsuma coupled KdV system. The meshfree algorithm is based on scattered data interpolation along with approximating functions known as radial basis functions (RBFs). The meshfree technique does not require space discretization. A set of scattered nodes provided by initial data is used for solution of the problem. Accuracy of the method is estimated in terms of the error norms L?, L_{?}, number of nodes in the domain of influence, time step size, parameter dependent and parameter independent RBFs, the numerical validation for the above mentioned three types of PDEs is given to check performance of the new approach.

Açıklama

URL: http://sjam.selcuk.edu.tr/sjam/article/view/281

Anahtar Kelimeler

Partial differential equations, Kısmi diferansiyel denklemler, Boussinesq system, Boussinesq sistemi, Drinefel’d-Sokolov-Wilson equations, Drinefel’d-Sokolov-Wilson denklemleri

Kaynak

Selcuk Journal of Applied Mathematics

WoS Q Değeri

Scopus Q Değeri

Cilt

12

Sayı

Künye

Uddin, M., Haq, S. (2011). Application of a numerical method using radial basis functions to nonlinear partial differential equations. Selcuk Journal of Applied Mathematics, 12 (1), 77-93.