The Heat Problem with Non-Local Boundary Conditions

Yıl 2024, Cilt: 7 Sayı: 2 , 61 - 68 , 27.12.2024

İrem Bağlan

https://doi.org/10.38061/idunas.1566513

https://izlik.org/JA33MF54UY

Öz

In this article, the two-dimensional inverse nonlinear parabolic problem is discussed. The most important feature of the problem was its solution with the Fourier approach. The solution was obtained by Fourier implicit and iteration method .

Anahtar Kelimeler

The higher problem , Fourier iterative method , nonlocal conditions , implicit finite-difference methods.

Kaynakça

• 1. Sharma, P.R., Methi, G. (2012). Solution of two-dimensional parabolic equation subject to non-local conditions using homotopy Perturbation method, Jour. of App.Com., 1, 12-16.
• 2. Cannon, J. Lin, Y. (1899). Determination of parameter p(t) in Hölder classes for some semi-linear parabolic equations, Inverse Problems, 4, 595-606.
• 3. Dehghan, M. (2005). Efficient techniques for the parabolic equation subject to nonlocal specifications, Applied Numerical Mathematics, 52(1), 39-62,2005.
• 4. Dehghan, M. (2001). Implicit Solution of a Two-Dimensional Parabolic Inverse Problem with Temperature Overspecification, Journal of Computational Analysis and Applications, 3(4). 5. Bağlan, I., Kanca, F. (2020). Solution of the boundary-value problem of heat conduction with periodic boundary conditions, Ukrainian Mathematical Journal, 72(2), 232-245.
• 6. Bağlan, I., Kanca, F. (2020). Two-dimensional inverse quasilinear parabolic problems with periodic boundary conditions of the boundary-value problem of heat conduction with periodic boundary conditions, Applicable Analysis, 98(8), 1549-1565. 7. Ionkin, N.I. (1977). Solution of a boundary value problem in heat conduction with a nonclassical boundary condition, Differential Equations, 13, 204-211.
• 8. Hill G.W. (1886), On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon, Acta Mathematica, 8,1-36.