An unconditionally stable modified leapfrog method for Maxwell's equation in Kerr-type nonlinear media

Research of numerical methods for solving Maxwell's equations in Kerr-type nonlinear media is quite popular. A so-called leapfrog alternating direction implicit (ADI) method which avoids mid-time computations is both unconditionally stable and computationally efficient, but hard to be applied to nonlinear problem. In this paper, we based on the difference between leapfrog method and leapfrog ADI method of linear Maxwell's equations, developed a modified leapfrog (ML) method for Maxwell's equations in Kerr-type nonlinear media. Stability and error estimate of the ML method are discussed. Numerical results have been achieved to verify the unconditional stability, and second-order convergence rate in both time and space, and ML method is more efficient than Crank-Nicolson (CN) method.