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Nada Abdul-Hassan Atiyah
Department of Mathematics, College of Education, Al-Qadisiyah University, Iraq
Aerospace Engineering Automotive Engineering Chemical Engineering, Chemistry & Bioengineering Civil Engineering, Building, Construction & Architecture Electrical & Electronics Engineering

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SPECTRAL DECOMPOSITION STRATEGIES FOR ANOMALOUS DIFFUSION AND IMPULSIVE BOUNDARY VALUE SYSTEMS Nada Abdul-Hassan Atiyah
Journal for Technology and Science Vol. 3 No. 3 (2026): Journal for Technology and Science
Publisher : PT ANTIS INTERNATIONAL PUBLISHER

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.61796/ipteks.v3i3.512

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.
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