Numerical Approach to Burgers’ Equation in Dusty Plasmas With Dust Charge Variation

Abstract

In this paper, the Crank-Nicholson method is applied to solve the one-dimensional nonlinear Burgers’ equation in warm, dusty plasmas with dust charge variation. After obtaining numerical results, a thorough analysis is conducted and compared against analytical solutions. On the basis of the comparison, it is evident that the numerical results obtained from the analysis are in good agreement with the analytical solution. The error between the analytical and numerical solutions of the Burgers’ equation is calculated by two error norms, namely L2 and L∞. A Von-Neumann stability analysis is performed on the present method, and it is found to be unconditionally stable according to the Von-Neumann analysis.

Keywords

• warm dusty plasmas
• burgers’ equation
• crank-nicolson method
• von neumann stability analysis