A numerical investigation of modified Burgers' equation in dusty plasmas with non-thermal ions and trapped electrons

In this paper, one-dimensional lower order modified Burgers' equation (MBE) in dusty plasmas having non-thermal ions and trapped electrons is investigated numerically by finite difference explicit method. The numerical results obtained by the finite difference explicit method for various values of the nonlinear and dissipative coefficients have been compared with the analytical solutions. The obtained numerical results are found to have good agreement with the analytical solutions. It is found that the nonlinear and dissipative coefficients have very important effect on the dust acoustic waves in the system. The absolute error between the analytical and the numerical solutions of the MBE is demonstrated. The stability condition is derived in terms of the equation parameters and the discretization using the von Neumann stability analysis. It has been observed that the waves become flatten and steeper when the dissipative coefficient decreases. It can be concluded that the finite difference explicit method is suitable and efficient method for solving the modified Burgers' equation.

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