Explicit FDTD method based on iterated Crank–Nicolson scheme

Abstract

Abstract An implicit Crank–Nicolson procedure can be replaced with an explicit iteration process. An explicit finite‐difference time‐domain method based on the iterated Crank–Nicolson scheme that has been widely used for solving Einstein's equations is newly developed. The formulation is presented with two iterations and its stability condition is also derived. Numerical results are found to agree well with those obtained from the traditional explicit finite‐difference time‐domain method, showing the validity of the present iterated Crank–Nicolson–finite‐difference time‐domain method.

Keywords

• Function theory, analysis
• Numerical approximation and analysis
• Interpolation and function approximation (numerical analysis)
• Differential equations (numerical analysis)
• Other numerical methods
• Numerical analysis