Second order monotone difference schemes with approximation on non-uniform grids for two-dimensional quasilinear parabolic convection-diffusion equations

Authors

  • Le Minh Hieu University of Economics, The University of Danang
  • Dang Ngoc Hoang Thanh
  • V.B. Surya Prasath

DOI:

https://doi.org/10.21638/11701/spbu01.2020.216

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 quasilinear 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.  

Keywords:

non-uniform grid, maximum principle, regularization principle, monotone difference scheme, convection-diffusion equation

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References

1. Самарский А. А. Теория разностных схем. М.: Наука, 1989.

2. Самарский А. А., Гулин А. А. Численные методы. М.: Наука, 1989.

3. Матус П. П., Во Тхи Ким Туен, Гаспар Ф. Монотонные разностные схемы для линейного параболического уравнения с граничными условиями смешанного типа // Доклады НАН Беларуси. 2014. Т. 58, № 5. С. 18-22.

4. Мажукин В. И., Малафей Д. А., Матус П. П., Самарский А. А. Р азностные схемы на неравномерных сетках для уравнений математической физики с переменными коэффициентами // ЖВМ и МФ. 2001. Т. 41, № 3. С. 407-419.

5. Малафей Д. А. Экономичные монотонные разностные схемы для многомерных задач конвенции-диффузии на неравномерных сетках // Докл. НАН Беларуси. 2000. Т. 44, № 4. С. 21-25.

6. Matus P. P., Poliakov D., Hieu L. M. On the consistent two-side estimates for the solutions of quasilinear convection-diffusion equations and their approximations on non-uniform grids // Journal of Computational and Applied Mathematics. 2018. Vol. 340. P. 571-581. DOI: 10.1016/j.cam.2017.09.020

7. Матус П. П., Хиеу Л. М., Волков Л. Г. Принцип максимума для разностных схем с непостоянными входными данными // Докл. НАН Беларуси. 2015. Т. 59, № 5. С. 13-17.

8. Friedman A. Partial differential equations of parabolic type. New York: Dover Publication Inc., 2013.

9. Samarskii A. A., Vabishchevich P. N., Matus P. P. Difference schemes with operator factors. Boston; Dordrecht; London: Kluwer Academic Publishers, 2002.

10. Prasath V. B. S., Moreno J. C. On convergent finite difference schemes for variational - PDE based image processing // Comp. Appl. Math. 2018. Vol. 37, no. 2. P. 1562-1580. DOI: 10.1007/s40314-016-0414-9

11. Koide S., Furihata D. Nonlinear and linear conservative finite difference schemes for regularized long wave equation // Japan J. Indust. Appl. Math. 2009. Vol. 26. Issue 1. Art. no. 15. DOI: 10.1007/BF03167544

12. Kalantari R., Shahmorad S. A Stable and Convergent Finite Difference Method for Fractional Black-Scholes Model of American Put Option Pricing // Comput. Econ. 2019. Vol. 53. Issue 1. P. 191- 205. DOI: 10.1007/s10614-017-9734-0

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Published

2020-08-15

How to Cite

Hieu, L. M., Thanh, D. N. H., & Prasath, V. S. (2020). Second order monotone difference schemes with approximation on non-uniform grids for two-dimensional quasilinear parabolic convection-diffusion equations. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7(2), 343–355. https://doi.org/10.21638/11701/spbu01.2020.216

Issue

Vol. 7 No. 2 (2020)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.