The use of radial basis functions by variable shape parameter for solving partial differential equations

Subject Areas : Statistics

H.  Nojavan ¹ (Department of Applied Mathematics, Faculty of Basic Science, Islamic Azad University, Science and Research Branch, Tehran, Iran)
S.  Abbasbandy ² (Department of Applied Mathematics, Faculty of Basic Science , Imam Khomeini International University, Qazvin, Iran)
T.  Allahviranloo ³ (Department of Applied Mathematics, Faculty of Basic Science, Islamic Azad University, Science and Research Branch, Tehran, Iran)

Received: 2018-02-18 Accepted : 2018-12-15 Published : 2019-04-01

Keywords: روش بدون شبکه موضعی, روش خطوط, توابع پایه‌ای نیوتن, هسته شعاعی به طور متغیر مقیاس , معادله غیرخطی برگرز,

Abstract :

In this paper, some meshless methods based on the local Newton basis functions are used to solve some time dependent partial differential equations. For stability reasons, used variably scaled radial kernels for constructing Newton basis functions. In continuation, with considering presented basis functions as trial functions, approximated solution functions in the event of spatial variable with collocation method. Then, with aid of method of lines obtained a system of ordinary differential equations according to solution function in the event of time. Methods applied for solving the nonlinear Burgers’ equation and couple Burgers’ equation. The numerical results show that the proposed method is efficient, accurate and stable.

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