Dynamical behaviour of non-linear Kuramoto-Sivashinskyequation using integrated radial basis function networks

In this research work, we implement the 1D-IRBFN method to find approximate solution of a very important non-linear partial differential equation (NLPDE) known as Kuramoto–Sivashinsky equation (KSE). The Crank–Nicolson formulation is used for time integration and the radial basis functions are used for the space discretization for KSE. We use the IRBFN method to solve two versions of KS equation, and then we compare numerical results with the exact solutions to demonstrate the accuracy of the method. The obtained solutions are in good agreement with the exact solutions. To visualize the dynamical behavior of KSE with different parameter values, we show graphical solutions and also compare the numerical solutions with few of results given in the recent research papers. To express the efficiency of the method, we calculate two types of errors in the numerical experiments (a) global relative error and (b) L2 error.Mathematics Subject Classification (2020) 74Sxx · 35G20