An approximate solution for PDEs of third order under mixed and nonlocal boundary conditions
*Mohammed A. J. Al-ShatrahCorresponding authormaliraqi279@gmail.comGeneral Directorate of Education Thi Qar, Ministry of EducationThi Qar, IraqView full profile → , M. S. Husseinmmmsh@sc.uobaghdad.edu.iqDepartment of MathematicsCollege of ScienceUniversity of BaghdadBaghdad, IraqView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 May 2025
- Published Online:
- 27 Jun 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2303
- Pages:
- 1211–1218
Abstract
Keywords
Subject Classifications
References
[1] Q. W. Ibraheem and M. S. Hussein, “Determination of time-dependent coefficient in time fractional heat equation,” Partial Differential Equations in Applied Mathematics, vol. 7, Art. no. 100492 (2023), doi: 10.1016/j.padiff.2023.100492.
[2] M. A. Rasheed and S. N. Kadhim, “Numerical solutions of two-dimensional vorticity transport equation using Crank–Nicolson method,” Baghdad Science Journal, vol. 19, no. 2, pp. 445–457 (2022), doi: 10.21123/bsj.2022.19.2.0445.
[3] M. A. Rasheed, S. Laverty, and B. Bannish, “Numerical solutions of a linear age-structured population model,” in AIP Conference Proceedings, vol. 2096, Art. no. 020002 (2019), doi: 10.1063/1.5097834.
[4] C. Ashyralyyev and M. Dedeturk, “Approximate solution of inverse problem for elliptic equation with overdetermination,” Abstract and Applied Analysis, vol. 2013, Art. no. 548017 (2013), doi: 10.1155/2013/548017.
[5] R. Kh. Amirov, Y. T. Mehraliyev, and N. A. Heydarzade, “On solvability of an inverse boundary value problem for the elliptic equation of second order with periodic and integral condition,” Cumhuriyet Science Journal, vol. 40, no. 2, pp. 355–368 (2019), doi: 10.17776/csj.535452.
[6] M. J. Huntul and I. Tekin, “On an inverse problem for a nonlinear third order in time partial differential equation,” Results in Applied Mathematics, vol. 15, Art. no. 100314 (2022), doi: 10.1016/j.rinam.2022.100314.
[7] J. A. Qahtan and M. S. Hussein, “Numerical solution to inverse coefficient problem for hyperbolic equation under overspecified condition of general integral type,” in AIP Conference Proceedings, vol. 2922, Art. no. 090003 (2024).
[8] J. A. Qahtan, M. S. Hussein, and T. E. Dyhoum, “An approximate solution for a second order elliptic inverse coefficient problem with nonlocal integral,” Ibn Al-Haitham Journal for Pure and Applied Sciences, vol. 37, no. 2, pp. 233–245 (2024).
[9] M. S. Hussein, T. E. Dyhoum, S. O. Hussein, and M. Qassim, “Identification of time-wise thermal diffusivity and advection velocity on the free-boundary inverse coefficient problem,” Mathematics, vol. 12, no. 17, Art. no. 2629 (2024), doi: 10.3390/math12172629.
[10] S. S. Weli and M. S. Hussein, “Finding timewise diffusion coefficient from nonlocal integral condition in one-dimensional heat equation,” in AIP Conference Proceedings, vol. 2922, Art. no. 090006 (2024).
[11] S. Gani and M. S. Hussein, “A fourth order pseudoparabolic inverse problem to identify the time dependent potential term from extra condition,” Iraqi Journal of Science, vol. 65, no. 8, pp. 4529–4549 (2024), doi: 10.24996/ijs.2024.65.8.32.
[12] Q. W. Ibraheem and M. S. Hussein, “Determination of time-dependent coefficient in inverse coefficient problem of fractional wave equation,” in AIP Conference Proceedings, vol. 2922, Art. no. 090004 (2024).
[13] Q. W. Ibraheem and M. S. Hussein, “Determination of timewise-source coefficient in time-fractional reaction–diffusion equation from first order heat moment,” Iraqi Journal of Science, vol. 65, no. 3, pp. 1612–1628 (2024), doi: 10.24996/ijs.2024.65.3.30.
[14] S. Gani and M. S. Hussein, “Numerical identification of timewise dependent coefficient in hyperbolic inverse problem,” Advances in the Theory of Nonlinear Analysis and Its Applications, vol. 7, no. 4, pp. 148–169 (2023).
[15] S. Gani, M. S. Hussein, and T. E. Dyhoum, “Timewise-dependent coefficients identification problems for third-order pseudo-parabolic equations from nonlocal extra conditions,” Ibn Al-Haitham Journal for Pure and Applied Sciences, vol. 38, no. 1, pp. 1–15 (2025).
[16] Z. S. Aliyev, Y. T. Mehraliyev, and E. H. Yusifova, “On some nonlocal inverse boundary problem for partial differential equations of third order,” Turkish Journal of Mathematics, vol. 45, no. 4, pp. 1871–1886 (2021), doi: 10.3906/mat-2101-45.
[17] M. Koorapetse and P. Kaelo, “An efficient hybrid conjugate gradient-based projection method for convex constrained nonlinear monotone equations,” Journal of Interdisciplinary Mathematics, vol. 22, no. 6, pp. 1031–1050 (2019), doi: 10.1080/09720502.2019.1700889.




