### Abstract

A new explicit time stepping scheme for electromagnetic simulations is described, the neo-finite-difference method. This numerical method which describes the time derivative as an arc instead of a straight line is more accurate. Thus, larger time steps can be used than with the standard leapfrog method. We start by Fourier analyzing the electromagnetic field in space. The Fourier amplitudes obey harmonic oscillator equations in time. The method involves approximating the time advance of a mode's amplitude from oscillator solutions for its estimated frequencies. From a computational point of view this involves replacing Δt by 2sin[ω^{E}(k)Δt/2]/ω^{E}(k) in the finite difference equations, where ω^{E}(k) is the estimated frequency of mode k; that is, Δt is multiplied by a k-dependent correction constant. The method not only improves the accuracy of the time stepping algorithm, but it increases the size of Δt for which it is stable. The ion-ripple laser is used as an example of a neo-finite difference electromagnetic simulation application to illustrate the new scheme. The size of the time step in the new scheme may be chosen one order of magnitude larger than for the standard method, The new scheme does not change the computation time per time step end only requires slight changes to the original code.

Original language | English |
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Pages (from-to) | 86-91 |

Number of pages | 6 |

Journal | Journal of Computational Physics |

Volume | 118 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1995 Apr 1 |

### All Science Journal Classification (ASJC) codes

- Numerical Analysis
- Modelling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics

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## Cite this

*Journal of Computational Physics*,

*118*(1), 86-91. https://doi.org/10.1006/jcph.1995.1081