CRANK-NICOLSON DIFFERENCE SCHEME FOR REVERSE
PARABOLIC NONLOCAL PROBLEM WITH INTEGRAL
AND NEUMANN BOUNDARY CONDITIONS

Abstract

In this paper, we study Crank-Nicholson difference scheme for approximate solutions of parabolic nonlocal reverse problem with integral and Neumann boundary conditions. Stability estimates for its solution are established. Via Mathlab framework, we give numerical example with explanation on computer realization.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 2
Year: 2021

DOI: 10.12732/ijam.v34i2.5

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References

  1. [1] R.K.M. Aldulaimi, An innovative receiver design for a parabolic trough solar collector using overlapped and reverse flow: An experimental study, Arabian Journal for Science and Engineering, 44, No 9 (2019), 7529-7539.
  2. [2] A. Ashyralyev, A. Dural and Y. Sozen, On well-posedness of the second order accuracy difference scheme for reverse parabolic equation, Malays. J. Math. Sci., 6 (2012), 91-109.
  3. [3] A. Ashyralyev and P.E. Sobolevskii, Well-Posedness of Parabolic Difference Equations, Birkh¨auser, Basel, Switzerland (1994).
  4. [4] C. Ashyralyyev, Well-posedness of boundary value problems for reverse parabolic equation with integral condition, e-Journal of Analysis and Applied Mathematics, 2018, No 1 (2018), 11-20.
  5. [5] C. Ashyralyyev, Stability of Rothe difference scheme for the reverse parabolic problem with integral boundary condition, Math. Meth. Appl. Sci., 43 (2020), 5369-5379.
  6. [6] C. Ashyralyyev, The second order of ADS for reverse parabolic boundary value problem with integral condition, Proceedings of the Institute of Mathematics and Mechanics, NASA, 46, No 2 (2020), 346-359.
  7. [7] C. Ashyralyyev, A. Dural and Y. Sozen, Finite difference method for the reverse parabolic problem with Neumann condition, In: AIP Conf. Proc. 1470 (1st Int. Conf. on Analysis and Applied Mathematics (ICAAM)), Gumushane, Turkey, Oct. 18-21, 2012 (Edited by: A. Ashyralyev and A. Lukashov), Amer. Inst. Physics (2012), 102-105.
  8. [8] D.N. Hao, N.V. Duc and N.V. Thang, Backward semi-linear parabolic equations with time-dependent coefficients and local Lipschitz source, Inverse Problems, 34, No 5 (2018). 282 C. Ashyralyyev, A. G¨onen¸c
  9. [9] D. Ijacu and M. Marinescu, Filtering for non-markovian SDEs involving nonlinear SPDEs and backward parabolic equations, Appl. Math. Optim., 70, No 3 (2014), 395-409.
  10. [10] T. Klimsiak, Strong solutions of semilinear parabolic equations with measure data and generalized backward stochastic differential equation, Potential Anal., 36, No 2 (2012) 373-404.
  11. [11] S.G. Krein, Linear Differential Equations in Banach Space, Nauka, Moscow (1966).
  12. [12] A. Lachapelle, J. Salomon and G. Turinici, Computation of mean field equilibria in economics, Math. Models Methods Appl. Sci., 20, No 4 (2010), 567-588.
  13. [13] J. Martin-Vaquero and J. Vigo-Aguiar, On the numerical solution of the heat conduction equations subject to nonlocal conditions, Appl. Numer. Math., 59 (2009), 2507-2514.
  14. [14] A.A. Samarskii, The Theory of Difference Schemes, New York, Dekker (2001).
  15. [15] P.E. Sobolevskii, Difference Methods for the Approximate Solution of Differential Equations, Voronezh State University Press, Voronezh (1975).
  16. [16] B.L.T. Thanh, F. Smarrazzo and A. Tesei, Sobolev regularization of a class of forward backward-parabolic equations, J. Differential Equations, 257 (2014), 1403-1456.