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

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.