JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (2): 114-126.doi: 10.6040/j.issn.1671-9352.0.2023.518

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Differential spectral approximation based on a dimensionality reduction for the fourth-order parabolic problem

WANG Junlin, HU Xiaoping, AN Jing*   

  1. School of Mathematical Science, Guizhou Normal University, Guiyang 550025, Guizhou, China
  • Published:2025-02-14

Abstract: This paper presents a differential spectral approximation for a fourth-order parabolic problem on a spherical domain based on a dimension reduction scheme. The fourth-order parabolic problem is transformed into an equivalent form in the spherical coordinates. By utilizing the properties of the Laplace-Beltrami operator and the orthogonality of the spherical harmonic functions, the problem is further decomposed into a series of decoupled one-dimensional fourth-order parabolic problems. Based on each one-dimensional fourth-order parabolic problem, its fully discrete scheme is established, and its stability and error estimation of the approximate solution are proved. Some numerical examples are given. The numerical results are shown that the differential spectral approximation algorithm is stable and convergent.

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