%0 Journal Article
%T A numerical method for KdV equation using rational radial basis functions
%J Computational Methods for Differential Equations
%I University of Tabriz
%Z 2345-3982
%A Shiralizadeh, Mansour
%A AliPanah, Amjad
%A Mohammadi, Maryam
%D 2023
%\ 04/01/2023
%V 11
%N 2
%P 303-318
%! A numerical method for KdV equation using rational radial basis functions
%K KdV equation
%K RBF
%K rational radial basis function method
%K Runge-Kutta method
%R 10.22034/cmde.2022.51967.2171
%X 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.
%U https://cmde.tabrizu.ac.ir/article_15500_a836ec06443e749fe92e9f3da7d0080e.pdf