A novel analytical approach to solve some applications of nonlinear problems

Altaie, Huda Omran; Shihab, Buthyna Najad; Khalaf, Hatam Y.

doi:10.47974/JIM-2539

Open Access Research Article

A novel analytical approach to solve some applications of nonlinear problems

^*Huda Omran AltaieCorresponding authorhuda.h.o@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure Science (Ibn Al-Haitham)University of BaghdadBaghdad, 10071, IraqView full profile → , Buthyna Najad Shihabbothaina.n.s@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure Science (Ibn Al-Haitham)University of BaghdadBaghdad, 10071, IraqView full profile → , Hatam Y. Khalafhatim.y.k@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure Science (Ibn Al-Haitham)University of BaghdadBaghdad, 10071, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 1503–1507Vol. 29Issue 5-BMay 2026DOI: 10.47974/JIM-2539XML

Received:: 01 Nov 2025
Published Online:: 27 Jun 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2539
Pages:: 1503–1507

Abstract

The Temimi and Ansari Technique (TAM), a new and powerful analytical method, has been proposed for solving nonlinear problems. As demonstrated by the findings, the method converges to the correct solution while handling nonlinear problems elegantly, accurately, and comfortably. The TAM result shows suggested methods are accurated and effective. The TAM-obtained solution is close to the actual solution. In addition, this approach is uncomplicated, derivative-free, easy to use, comfortable, and requires minimal computing power. To show how well the recommended approach applies, the solution graphs are displayed.

Keywords

Semi-analytical method Temimi and Ansari method Analytical method Perturbation methods

Subject Classifications

35R1135R60

References

[1] H. Altaie, “Performance of two-way nesting techniques for shallow water models,” International Journal of Mechanical Engineering and Technology, vol. 7, no. 6, pp. 425-434 (2016).
[2] O. A. Salman and H. O. Altaie, “Analytical approximate solutions of random integro differential equations with Laplace decomposition method,” Journal of Interdisciplinary Mathematics, vol. 27, no. 4, pp. 907-912 (2024).
[3] A. M. Mohammed and H. O. Altaie, “Analytical solutions via coupled Elzaki adomian decomposition method for some applications,” Journal of Interdisciplinary Mathematics, vol. 27, no. 4, pp. 761-766 (2024).
[4] O. Ragb, L. F. Seddek, and M. S. Matbuly, “Iterative differential quadrature solutions for Bratu problem,” Computers & Mathematics with Applications, vol. 74, no. 2, pp. 249–257 (2017).
[5] A. M. Mohammed and H. O. Altaie, “Elzaki transform decomposition approach to solve Riccati matrix differential equations,” Journal of Interdisciplinary Mathematics, vol. 27, no. 4, pp. 767-773 (2024).
[6] M. A. Z. Raja and S. U. I. Ahmad, “Numerical treatment for solving one-dimensional Bratu problem using neural networks,” Neural Computing and Applications, vol. 24, no. 3, pp. 549–561 (2014).
[7] H. Günerhan, “Analytical and approximate solution of two-dimensional convection-diffusion problems,” An International Journal of Optimization and Control: Theories & Applications (IJOCTA), vol. 10, no. 1, pp. 73–77 (2020).
[8] H. Temimi and A. R. Ansari, “A computational iterative method for solving nonlinear ordinary differential equations,” LMS Journal of Computation and Mathematics, vol. 18, no. 1, pp. 730-753 (2015).
[9] H. Temimi and A. R. Ansari, “A semi-analytical iterative technique for solving nonlinear problems,” Computers & Mathematics with Applications, vol. 61, no. 2, pp. 203–210 (2011).
[10] S. A. Al-Ameedee, H. A. Ahmed, and A. J. Obaid, “Differential subordinations of meromorphic multivalent harmonic functions,” Journal of Interdisciplinary Mathematics, vol. 27, no. 4, pp. 947–952 (2024), doi: 10.47974/JIM-1915.
[11] H. Temimi and A. R. Ansari, “A new iterative technique for solving nonlinear second order multi-point boundary value problems,” Applied Mathematics and Computation, vol. 218, no. 4, pp. 1457–1466 (2011).

Views: 60Downloads: 85Citations: 0