Atiyah, Nada Abdul-Hassan (2026) SPECTRAL DECOMPOSITION STRATEGIES FOR ANOMALOUS DIFFUSION AND IMPULSIVE BOUNDARY VALUE SYSTEMS. Journal for Technology and Science, 3 (3). ISSN 3047-4337

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Abstract

Objective: Physical models with memory or impulsive effects of non-local nature present complications mathematically. Method: To circumvent such computational challenges, a frequency domain approach is explored herein. The new algorithm allows one to deal easily with fractional derivatives and strong singularities by reducing the problem of solving the integro-differential equation to the solution of an algebraic problem. Results: Numerical analysis suggests that the transition to the frequency domain is indeed valid but exhibits a noticeable reduction in rate of convergence, which goes from O(N⁻²) in normal situations to O(N⁻ᵅ) for the anomalous case. We further consider sustained oscillations induced by impulse-like forcing. Novelty: The traditional approach using finite difference method is known to have stability issues when dealing with anomalous diffusion as well as impulses like Dirac delta functions.

Item Type:	Article
Uncontrolled Keywords:	Spectral decomposition, Anomalous transport, Non-integer operators, Impulsive dynamics, Frequency domain analysis, Oscillatory artifacts, Fundamental solutions
Subjects:	H Social Sciences
Depositing User:	admin eprints
Date Deposited:	02 Jul 2026 03:35
Last Modified:	02 Jul 2026 03:35
URI:	http://eprints.umsida.ac.id/id/eprint/16727

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