A numerical method for KdV equation using rational radial basis functions

Document Type : Research Paper


1 Department of Mathematics, Payame Noor University (PNU), Tehran, Iran.

2 Department of Applied Mathematics, University of Kurdistan, Sanandaj, Iran.

3 Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran.


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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Volume 11, Issue 2
April 2023
Pages 303-318
  • Receive Date: 06 June 2022
  • Revise Date: 23 October 2022
  • Accept Date: 30 October 2022
  • First Publish Date: 30 October 2022