Stability and dispersion analysis of ADI-MRTD and ADI high-order schemes

M. K. Sun, Wai Yip Tam

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)


The maximum time-step size of the alternating-direction implicit finite-differenc̀e time-domain (ADI-FDTD) method is not limited by the Courant-Friedrich-Levy (CFL) stability condition. However, the numerical-dispersion error of the ADI-FDTD method is much greater than that of Yee's FDTD method. In this paper, the numerical dispersion is improved by approximating the spatial derivatives using cubic spline Battle-Lemarie scaling functions and the high-order centered differences. The stability condition and the numerical-dispersion relations are derived using the Fourier series method and validated by a numerical simulation. The new scheme is unconditionally stable and the numerical dispersion error can be reduced to the limit of the conventional ADI-FDTD method with the 6th-order centered difference.
Original languageEnglish
Pages (from-to)43-46
Number of pages4
JournalMicrowave and Optical Technology Letters
Issue number1
Publication statusPublished - 5 Apr 2005


  • ADI FDTD method
  • Battle-Lemarie scaling functions
  • High-order centered finite difference
  • Numerical dispersion

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics
  • Electrical and Electronic Engineering


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