Simulation of generalized time fractional Gardner equation utilizing in plasma physics for non-linear propagation of ion-acoustic waves

Abstract

In this work, radial basis function collocation method (RBFCM) is implemented for generalized time fractional Gardner equation (GTFGE). The RBFCM is meshless and easy-to-implement in complex geometries and higher dimensions, therefore, it is highly demanding. In this work, the Caputo derivative of fractional order ? ? (0, 1] is used to approximate the first order time derivative whereas, Crank-Nicolson scheme is hired to approximate space derivatives. The numerical solutions are presented and discussed, which demonstrate that the method is effective and accurate.