Truncation and Convergence Dynamics: KdV Burgers Model in the Sense of Caputo Derivative

Abstract

This study examines the time fractional KdV Burgers equation with the initial conditions by using finite difference method (FDM) via the extended result on Caputo formula. For this reason, various fractional differential operators are defined and analyzed. In order to check the stability of the numerical scheme, the Fourier-von Neumann technique is used. By presenting an example of KdV Burgers equation above mentioned issues are discussed and numerical solutions of the error estimates are found for the FDM. For the errors in L-2 and L-infinity the method accuracy is controlled. Moreover, the obtained results are compared with the exact solution for different cases of non-integer order and the behavior of the potentials u is presented as a graph. The numerical results are shown in tables.