A numerical method for KdV equation using rational radial basis functions

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Shiralizadeh Mansour; Alipanah Amjad; MOHAMMADI MARYAM

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Journal Paper

Paper Information

Journal: Computational Methods for Differential Equations Year:2023 | Volume:11 | Issue:2 Page(s): 303-318

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Title

A numerical method for KdV equation using rational radial basis functions

Author(s)

Shiralizadeh Mansour | Alipanah Amjad | MOHAMMADI MARYAM | Issue Writer Certificate

Keywords

KdV equation

RBF

Rational radial basis function method

Runge-Kutta method

Abstract

In this paper, we use the rational radial basis functions ( RRBFs) method to solve the Korteweg-de Vries (KdV) equation, particularly when the equation has a solution with steep front or sharp gradients. We approximate the spatial derivatives by RRBFs method then we apply an explicit fourth-order Runge-Kutta method to advance the resulting semi-discrete system in time. Numerical examples show that the presented scheme preserves the conservation laws and the results obtained from this method are in good agreement with analytical solutions.

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APA: Copy

Shiralizadeh, Mansour, Alipanah, Amjad, & MOHAMMADI, MARYAM. (2023). A numerical method for KdV equation using rational radial basis functions. COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 11(2), 303-318. SID. https://sid.ir/paper/1057546/en

Vancouver: Copy

Shiralizadeh Mansour, Alipanah Amjad, MOHAMMADI MARYAM. A numerical method for KdV equation using rational radial basis functions. COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS[Internet]. 2023;11(2):303-318. Available from: https://sid.ir/paper/1057546/en

IEEE: Copy

Mansour Shiralizadeh, Amjad Alipanah, and MARYAM MOHAMMADI, “A numerical method for KdV equation using rational radial basis functions,” COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, vol. 11, no. 2, pp. 303–318, 2023, [Online]. Available: https://sid.ir/paper/1057546/en

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