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A split step approach for the 3-D Maxwell’s equations. (English) Zbl 1029.65094

Summary: Split-step procedures have previously been used successfully in a number of situations, e.g. for Hamiltonian systems, such as certain nonlinear wave equations. In this study, we note that one particular way to write the 3-D Maxwell’s equations separates these into two parts, requiring only the solution of six uncoupled 1-D wave equations. The approach allows arbitrary orders of accuracy in both time and space, and features in many cases unconditional stability.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
78A25 Electromagnetic theory (general)
78M20 Finite difference methods applied to problems in optics and electromagnetic theory
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L70 Second-order nonlinear hyperbolic equations
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