Back and forth error compensation and correction method for linear hyperbolic systems with application to the Maxwell's equations

Abstract We study the Back and Forth Error Compensation and Correction (BFECC) method for linear hyperbolic systems and in particular for the Maxwell's equations. BFECC has been applied to schemes for scalar advection equations to improve their stability and order of accuracy. Similar results have been established in this paper for linear hyperbolic systems with constant coefficients. We apply BFECC to the central difference scheme, Lax-Friedrichs scheme and a combination of them for the Maxwell's equations and obtain second order accurate schemes with large CFL numbers (greater than 1 in one or two dimensions). The method is further applied to schemes on non-orthogonal unstructured grids. The new BFECC schemes for the Maxwell's equations operate on a single non-staggered grid and are simple to implement on unstructured grids. Numerical examples are given to demonstrate the effectiveness of the new schemes.