JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (4): 16-28.doi: 10.6040/j.issn.1671-9352.0.2022.274

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Compact difference schemes for the fourth-order parabolic equations with the third Dirichlet boundary

HUANG Yu, GAO Guang-hua*   

  1. School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, Jiangsu, China
  • Published:2023-03-27

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Abstract: Based on some techniques involving the weighted average and high order Hermite interpolation, several useful differentiation formulae for approximating the fourth-order derivatives are derived along with the truncation error analyses. Then three high order compact difference schemes are proposed to solve the initial-boundary value problem of the fourth-order parabolic equations with the third Dirichlet boundary conditions. The unconditional stability is proved by the Fourier analysis method. Numerical experiments are carried out. The major difference of the proposed three schemes lies in the different numerical treatment of spatial derivatives near the boundary. The global accuracy of all presented schemes can attain the order of two in time and four in space.

Key words: fourth-order parabolic equation, third Dirichlet boundary condition, high accuracy, compact difference scheme, stability

CLC Number: 

  • O241.82
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