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Search results for , issue "Vol 8 No 2 (2026): November 2026" : 1 Documents clear
A Hybrid Semi-Analytical Technique for the Homogeneous Space Fractional Damped Wave Equation with Gaussian White Noise Abdulazeez, Sadeq Taha; İşleyen, Şakir; Jameel, Hasan Hazim
JURNAL DIFERENSIAL Vol 8 No 2 (2026): November 2026
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v8i2.27486

Abstract

This paper addresses the severely ill-posed final value problem for the homogeneous space fractional damped wave equation subject to Gaussian white noise. Unlike the well-posed forward problem, recovering the initial state from noisy final data is unstable, as high-frequency noise components are amplified exponentially. We propose the Laplace-Residual Power Series Method (LRPSM), a semi-analytical iterative technique, to solve this problem. By transforming the backward problem into a time-reversed initial value problem, we construct a series solution in the Laplace domain. We provide a rigorous theorem and proof regarding the convergence of the method for exact data and discuss its regularizing properties via series truncation for noisy data. A numerical example is presented to illustrate the accuracy and stability of the proposed method compared to standard Fourier truncation techniques.

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