An inverse problem of identifying the time‐dependent potential in a fourth‐order pseudo‐parabolic equation from additional condition. Issue 2 (8th April 2021)

• Record Type: Journal Article
• Authors: Huntul, Mousa J.; Tamsir, Mohammad; Dhiman, Neeraj
• Is Part Of: Numerical methods for partial differential equations. Volume 39:Issue 2(2023)
• Page Start: 848
• Page End: 865
• Publication Date: 2021-04-08
• Subjects: inverse identification problem -- nonlinear optimization -- pseudo‐parabolic equation -- QB‐spline collocation method -- Tikhonov regularization; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22778
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: The aim of this work is to identify numerically, for the first time, the time‐dependent potential coefficient in a fourth‐order pseudo‐parabolic equation with nonlocal initial data, nonlocal boundary conditions, and the boundary data as overdetermination condition. This problem emerges significantly in the modeling of various phenomena in physics and engineering. From literature we already know that this inverse problem has a unique solution. However, the problem is still ill‐posed by being unstable to noise in the input data. For the numerical realization, we apply the quintic B‐spline (QB‐spline) collocation method for discretizing the pseudo‐parabolic problem and the Tikhonov regularization for finding a stable and accurate solution. The resulting nonlinear minimization problem is solved using the MATLAB subroutine lsqnonlin . Moreover, the von Neumann stability analysis is also discussed.