Differential-difference equations with optimal parameters (Q6148037)

In this paper, the numerical solution of Maxwell's equations is considered based on a second-order finite-difference scheme containing optimal parameters. Then, some parameters are introduced into the second-order difference equation for Laguerre harmonics and their optimal values are determined by minimizing the error between the numerical solutions and the exact analytical solutions of the equations for harmonics. The differential-difference equations with difference in space and differential in time are obtained using finite-difference schemes of the second order of approximation in both time and space. Finally, a numerical example is given to show the effectiveness of the optimal finite-difference schemes.