Analysis of inverse problem for pseudo-hyperbolic equation under periodic boundary condition

İrem Bağlan; Akbala Yernazar; Erman Aslan; Hüseyin Budak; Miguel Vivas-Cortez

doi:10.1038/s41598-025-25105-1

Analysis of inverse problem for pseudo-hyperbolic equation under periodic boundary condition

Sci Rep. 2025 Nov 21;15(1):41218. doi: 10.1038/s41598-025-25105-1.

Authors

İrem Bağlan¹, Akbala Yernazar¹, Erman Aslan², Hüseyin Budak¹, Miguel Vivas-Cortez³

Affiliations

¹ Department of Mathematics, Kocaeli University, Kocaeli, 41001, Türkiye.
² Department of Mechanical Engineering, Kocaeli University, Kocaeli, 41001, Türkiye.
³ Faculty of Exact, Natural, and Environmental Sciences, Pontifical Catholic University of Ecuador, FRACTAL Laboratory (Fractional Research Analysis, Convexity, and their Applications Laboratory), Quito, Ecuador Av. 12 de Octubre 1076, Apartado, Quito, 17-01-2184, Ecuador. mjvivas@puce.edu.ec.

Abstract

This research paper investigates an inverse problem involving time-dependent unknown coefficients in a one-dimensional nonlinear pseudo-hyperbolic equation with nonlocal boundary conditions. The Fourier method is employed, and the convergence, uniqueness, and stability of the solution are demonstrated. Additionally, the Finite Difference Method (FDM) is applied to address the inverse problem numerically. A numerical example is provided to demonstrate the performance of the method. In the Finite Difference Method, two finite difference schemes with different levels of accuracy are used and compared with each other. Furthermore, the cases of ε = 0 (hyperbolic) and ε ≠ 0 (pseudo-hyperbolic) are also compared.

Keywords: Finite difference method; Fourier method; Inverse problem; Nonlinear pseudo-hyperbolic equation; Periodic boundary condition.