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Khan, I.R. and Ohba, R. (1999) Closed-Form Expressions for the Finite Difference Approximations of First and Higher Derivatives Based on Taylor Series. Journal of Computational and Applied Mathematics, 107, 179-193.
https://doi.org/10.1016/S0377-0427(99)00088-6

has been cited by the following article:

• TITLE: Two-Step Asymmetric Perfectly Matched Layer Model for High-Order Spatial FDTD Solver of 2D Maxwell’s Equations

  AUTHORS: Abdelrahman Mahdy

  KEYWORDS: Perfectly Matched Layer, The Finite-Difference-Time-Domain, Terahertz Radiation Production, Filamentation of Femtosecond Laser, Maxwell’s Equations Solver

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.2, February 25, 2025

  ABSTRACT: We implemented a two-step Asymmetric Perfectly Matched Layer (APML) model in High-Order Finite Difference Time Domain (FDTD) algorithm for solving two-dimensional Maxwell’s equations. Initially, we applied the APML method to the standard second-order FDTD algorithm to derive a two-step time-staggered APML (APML-2SS) and a two-step time-centered APML (APML-2SC) formulation for these equations, afterwards, we extended these formulations in high-order FDTD algorithm in order to derive a APML high-order FDTD (APML-HOFDTD) formulation for our Maxwell’s equations. To examine the performance and check out the accuracy of APML model, we conducted a numerical study using a 2D fluid where the three derived formulations were to analyze selected phenomena in terahertz radiation production by the filamentation of two femtosecond laser beams in air plasma. Numerical results illustrated that the two-step APML model is sufficiently accurate for solving our 2D Maxwell’s equations in high-order FDTD discretization and it demonstrated a great performance in studying the THz radiation production.