Numerical Simulation and Analysis of the Modified Burgers' Equation in Dusty Plasmas

Abstract

This paper presents a comprehensive study of the numerical simulation of the one-dimensional modified Burgers' equation in dusty plasmas. The reductive perturbation method is employed to derive the equation, and a numerical solution is obtained using the explicit finite difference technique. The obtained results are extensively compared with analytical solutions, demonstrating a high level of agreement, particularly for lower values of the dissipation coefficient. The accuracy and efficiency of the technique are evaluated based on the absolute error. Additionally, the accuracy and effectiveness of the technique are assessed by plotting L2 and L∞ error graphs. The technique's reliability is further confirmed through von Neumann stability analysis, which indicates that the technique is conditionally stable. Overall, the study concludes that the proposed technique is successful and dependable for numerically simulating the modified Burgers' equation in dusty plasmas.

Keywords

• Dusty plamas
• Reductive perturbation method
• Modified Burgers equation
• Finite difference explicit technique
• von Neumann stability analysis