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Second Order Monotone Difference Schemes with Approximation on Non-Uniform Grids for Two-Dimensional Quasilinear Parabolic Convection-Diffusion Equations

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Abstract

The present communication is devoted to the construction of monotone difference schemes of the second order of local approximation on non-uniform grids in space for 2D quasi-linear parabolic convection-diffusion equation. With the help of difference maximum principle, two-sided estimates of the difference solution are established and an important a priori estimate in a uniform norm C is proved. It is interesting to note that the maximal and minimal values of the difference solution do not depend on the diffusion and convection coefficients.

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Author information

Authors and Affiliations

  1. University of Economics, The University of Danang, 550000, Da Nang, Vietnam

    Le M. Hieu

  2. Department of Information Technology, School of Business Information Technology, University of Economics Ho Chi Minh City, 700000, Ho Chi Minh City, Vietnam

    Dang N. H. Thanh

  3. Division of Biomedical Informatics, Cincinnati Children’s Hospital Medical Center, 45229, Cincinnati, OH, USA

    V. B. Surya Prasath

  4. Department of Pediatrics, University of Cincinnati, 45267, Cincinnati, OH, USA

    V. B. Surya Prasath

  5. Department of Biomedical Informatics, College of Medicine, University of Cincinnati, 45267, Cincinnati, OH, USA

    V. B. Surya Prasath

  6. Department of Electrical Engineering and Computer Science, University of Cincinnati, 45221, Cincinnati, OH, USA

    V. B. Surya Prasath

Authors
  1. Le M. Hieu
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  2. Dang N. H. Thanh
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  3. V. B. Surya Prasath
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Corresponding authors

Correspondence to Le M. Hieu, Dang N. H. Thanh or V. B. Surya Prasath.

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Hieu, L.M., Thanh, D.N. & Surya Prasath, V.B. Second Order Monotone Difference Schemes with Approximation on Non-Uniform Grids for Two-Dimensional Quasilinear Parabolic Convection-Diffusion Equations. Vestnik St.Petersb. Univ.Math. 53, 232–240 (2020). https://doi.org/10.1134/S1063454120020107

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  • DOI: https://doi.org/10.1134/S1063454120020107

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