High-order difference schemes for 2D elliptic and parabolic problems with mixed derivatives

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14 Citations (Scopus)

Abstract

We propose a 9-point fourth-order finite difference scheme for 2D elliptic problems with a mixed derivative and variable coefficients. The same approach is extended to derive a class of two-level high-order compact schemes with weighted time discretization for solving 2D parabolic problems with a mixed derivative. The schemes are fourth-order accurate in space and second- or lower-order accurate in time depending on the choice of a weighted average parameter μ. Unconditional stability is proved for 0.5 ≤ μ, ≤ 1, and numerical experiments supporting our theoretical analysis and confirming the high-order accuracy of the schemes are presented.

Original languageEnglish
Pages (from-to)366-378
Number of pages13
JournalNumerical Methods for Partial Differential Equations
Volume23
Issue number2
DOIs
Publication statusPublished - Mar 2007

Fingerprint

High-order Schemes
Parabolic Problems
Difference Scheme
Elliptic Problems
Fourth Order
High-order Compact Scheme
Derivatives
Unconditional Stability
Derivative
High Order Accuracy
Weighted Average
Time Discretization
Variable Coefficients
Finite Difference Scheme
Theoretical Analysis
Numerical Experiment
Experiments
Class

Keywords

  • Compact scheme
  • Elliptic problems
  • Mixed derivative
  • Parabolic problems
  • Stability

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Mathematics

Cite this

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abstract = "We propose a 9-point fourth-order finite difference scheme for 2D elliptic problems with a mixed derivative and variable coefficients. The same approach is extended to derive a class of two-level high-order compact schemes with weighted time discretization for solving 2D parabolic problems with a mixed derivative. The schemes are fourth-order accurate in space and second- or lower-order accurate in time depending on the choice of a weighted average parameter μ. Unconditional stability is proved for 0.5 ≤ μ, ≤ 1, and numerical experiments supporting our theoretical analysis and confirming the high-order accuracy of the schemes are presented.",
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AB - We propose a 9-point fourth-order finite difference scheme for 2D elliptic problems with a mixed derivative and variable coefficients. The same approach is extended to derive a class of two-level high-order compact schemes with weighted time discretization for solving 2D parabolic problems with a mixed derivative. The schemes are fourth-order accurate in space and second- or lower-order accurate in time depending on the choice of a weighted average parameter μ. Unconditional stability is proved for 0.5 ≤ μ, ≤ 1, and numerical experiments supporting our theoretical analysis and confirming the high-order accuracy of the schemes are presented.

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KW - Stability

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