GALERKIN FINITE ELEMENT METHOD AND FINITE DIFFERENCE METHOD FOR SOLVING CONVECTIVE NON-LINEAR EQUATION

The fast progress has been observed in the development of numerical and analytical techniques for solving convection-diffusion and fluid mechanics problems. Here, a numerical approach, based in Galerkin Finite Element Method with Finite Difference Method is presented for the solution of a class of non-linear transient convection-diffusion problems. Using the analytical solutions and the L2 and L∞ error norms, some applications is carried and valuated with the literature

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

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