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October 27, 2025Journal of Al-Qadisiyah for Computer Science and MathematicsOpen Access

Distributional Solutions to Boundary Value Problems Using Fourier Series

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NANada Abdul-Hassan Atiyah

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Overview

Analysis reveals effective solutions to boundary value problems with fractional derivatives, indicating improvements in computational efficiency via Fourier series.

Key Points

  • Fast convergence of Fourier series for smooth forcing terms enhances numerical method efficiency, thereby addressing complex boundary value problems.
  • Key results illustrate Fourier series' capability to manage fractional derivatives, solving significant issues in mathematical physics and engineering.
  • Observational analysis highlights Gibbs phenomena challenges for non-smooth inputs within boundary value problems, showcasing practical limitations.
  • The framework transforms differential operators into algebraic forms in the frequency domain, enabling accurate solutions for various applications.

Cite This Study

Nada Abdul-Hassan Atiyah (2025) studied this question.

synapsesocial.com/papers/68ff87e2c8c50a61f2bdce99https://doi.org/10.29304/jqcsm.2025.17.32416
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