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New Shift-Map Parabolic Equations Based on Finite Difference Method
  • Nuanfeng Zhang,
  • Yunliang Long
Nuanfeng Zhang

Corresponding Author:[email protected]

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Yunliang Long


In this paper, a new type of shift-map PE is proposed, which fundamentally overcomes fatal defect in [14]'s solutions, as they are inaccurate for waves propagating at angles close to 0 •. According to both theory and experiment, [14]'s 1storder solution is not accurate for waves propagating at 0 •. Additionally, the reduced function of [14] introduces truncation error for the wave propagating at angle close to 0 •. These shortcomings render the PE unsuitable for the wave propagating problem. The proposed method utilizes the usual reduced function to eliminate the truncation error when the wave propagates at 0 • and reduces the truncation errors when the wave propagating at angle close to 0 •. Two examples of new shift-map PE are studied and compared to [14]'s methods. Both theory and experiments demonstrate that the proposed methods achieve higher accuracy while using a larger range step compared to [14]'s solutions, making it more suitable for long-distance calculation than [14]'s methods. In the numerical experiments, the proposed method with the range step of 128λ is more accurate than [14]'s solution with the range step of 1λ.
13 Jan 2024Submitted to TechRxiv
25 Jan 2024Published in TechRxiv