An Efficient Meshfree Numerical Technique to Solve Fractional Schamel–KdV Equation for Ion-Acoustic Solitary Waves in Dusty Plasma

The Schamel–KdV equation plays a vital role in studying the effect of electron trapping on the nonlinear interaction of ion-acoustic waves in plasma and dusty plasma. This work presents a numerical scheme-based radial basis function-finite difference (RBF-FD) method to solve the time-fractional Schamel–KdV equation. The advantages of using this method are their meshfree nature and flexibility in dealing with complex geometries. In the discretization process, a finite difference (FD) technique is used to discretize the temporal derivative, while the multiquadric (MQ) RBF is used to approximate the spatial derivatives. The theoretical convergence and stability analysis of the time-discrete scheme are also established. In addition, numerical experiments are executed through some illustrated problems, and the obtained results are compared with that acquired by the tanh method and Kudryashov method solutions to show the high accuracy and plausibility of the proposed technique. Also, the graphical representations are given to demonstrate the physical interpretation of the resulting wave structures.