A numerical method for KdV equation using rational radial basis functions
نویسندگان
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.
doi
10.22034/cmde.2022.51967.2171چکیده
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.
