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

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Nojavan h.; ABBASBANDY S.; ALLAHVIRANLOO T.

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Paper Information

Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2019 | Volume:5 | Issue:17 Page(s): 17-38

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Title

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

Author(s)

Nojavan h. | ABBASBANDY S. | ALLAHVIRANLOO T. | Issue Writer Certificate

Keywords

Local meshless methodQ1

Method of linesQ1

Newton basis functionsQ1

Variably scaled radial kernelQ1

Burgers’equationQ1

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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APA: Copy

Nojavan, h., ABBASBANDY, S., & ALLAHVIRANLOO, T.. (2019). The use of radial basis functions by variable shape parameter for solving partial differential equations. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 5(17 ), 17-38. SID. https://sid.ir/paper/257334/en

Vancouver: Copy

Nojavan h., ABBASBANDY S., ALLAHVIRANLOO T.. The use of radial basis functions by variable shape parameter for solving partial differential equations. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2019;5(17 ):17-38. Available from: https://sid.ir/paper/257334/en

IEEE: Copy

h. Nojavan, S. ABBASBANDY, and T. ALLAHVIRANLOO, “The use of radial basis functions by variable shape parameter for solving partial differential equations,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 5, no. 17 , pp. 17–38, 2019, [Online]. Available: https://sid.ir/paper/257334/en

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