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Shiralizadeh, Mansour, AliPanah, Amjad, Mohammadi, Maryam. (1402). A numerical method for KdV equation using rational radial basis functions. سامانه مدیریت نشریات علمی, 11(2), 303-318. doi: 10.22034/cmde.2022.51967.2171
Mansour Shiralizadeh; Amjad AliPanah; Maryam Mohammadi. "A numerical method for KdV equation using rational radial basis functions". سامانه مدیریت نشریات علمی, 11, 2, 1402, 303-318. doi: 10.22034/cmde.2022.51967.2171
Shiralizadeh, Mansour, AliPanah, Amjad, Mohammadi, Maryam. (1402). 'A numerical method for KdV equation using rational radial basis functions', سامانه مدیریت نشریات علمی, 11(2), pp. 303-318. doi: 10.22034/cmde.2022.51967.2171
Shiralizadeh, Mansour, AliPanah, Amjad, Mohammadi, Maryam. A numerical method for KdV equation using rational radial basis functions. سامانه مدیریت نشریات علمی, 1402; 11(2): 303-318. doi: 10.22034/cmde.2022.51967.2171

A numerical method for KdV equation using rational radial basis functions

Computational Methods for Differential Equations
مقاله 8، دوره 11، شماره 2، تیر 2023، صفحه 303-318    اصل مقاله (1.14 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.51967.2171
نویسندگان
Mansour Shiralizadeh* 1؛ Amjad AliPanah2؛ Maryam Mohammadi3
1Department of Mathematics, Payame Noor University (PNU), Tehran, Iran.
2Department of Applied Mathematics, University of Kurdistan, Sanandaj, Iran.
3Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran.
چکیده
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. 
کلیدواژه‌ها
KdV equation؛ RBF؛ Rational radial basis function method؛ Runge-Kutta method
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