Filter Regularization Method for an Inverse Problem of Over-damped Harmonic Oscillator Equation
DOI:
https://doi.org/10.22399/ijcesen.5212Keywords:
Filter regularization method, Harmonic oscillator equation, ill posed problem, inverse problemAbstract
In many fields of applied mathematics and physics, inverse problems involving the harmonic oscillator are common. These problems are often ill-posed in the sense of Jacques Hadamard, where minor changes in the data can result in significant deviations in the solution. In this work, we study an ill-posed inverse problem related to the harmonic oscillator equation with the aim of reconstructing unknown parameters from noisy and indirect observations.We suggest a technique of regularization to address the instability present in this class of problems. Convergence results are obtained under appropriate assumptions on the regularization parameter and noise level, and the regularized problem’s well posed-ness is established. Furthermore, error estimates are obtained to measure how stable the suggested method is. The efficiency and resilience of the approach in recovering stable approximations of the intended solution are illustrated through numerical simulations. The obtained results verify that the suggested regularization technique provides a dependable and effective method for resolving harmonic oscillator inverse problems.
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