Proceedings of International Conference on Applied Innovation in IT  ·  2026/06/12  ·  Vol. 14  ·  Issue 4  ·  pp. 287–297
Numerical Identification of Time-Varying Coefficient for
Anam Alwan Salih and Mohammed Sabah Hussein
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Abstract
This article refers to the integral numerical analysis of the inverse boundary-value problem for a pseudohyperbolic equation, incorporating an additional integral condition. While the theoretical uniqueness of the solution has been established, the problem remains ill-posed due to its high sensitivity to small variations in the input data. To address this, the study employs the Crank-Nicolson finite difference method for both temporal and spatial discretization, combined with Tikhonov regularization to ensure the stability of the inversion process. The regularization parameter is judiciously chosen to strike an optimal balance between stability and accuracy. The resulting nonlinear minimization task is addressing MATLAB’s lsqnonlin function, applied to both exact and noise-effected data sets. A Von Neumann stability analysis confirms the robustness of the numerical scheme. Computational findings reveal that the proposed method delivers precise and stable result, even in the presence of noisy data. This work marks the first practical numerical solution to this inverse problem, demonstrating the efficacy of combining finite-difference discretization with Tikhonov regularization, thereby providing a solid foundation for future numerical and applied investigations within this domain of boundary-value problems.
Keywords
Inverse Boundary-Value Problem Pseudohyperbolic Equation; Additional Integral Condition Tikhonov Regularization Nonlinear Optimization
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