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Spectral Solutions of the Second-Kind Volterra Integral Equations using Vieta-Fibonacci Operational Matrix |
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PP: 169-179 |
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doi:10.18576/amis/200112
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Author(s) |
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Nasser H. Sweilam,
Adel Abdelfattah Darwish,
Doaa Gamal Mohamed,
Aliaa Ali Fath-Elbab,
Adel Abd Elaziz El-Sayed,
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Abstract |
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| In this research, we propose a numerical method to compute approximate solutions for second-kind Volterra integral equations (VIEs) and systems of such equations. The VIEs are converted into a system of algebraic equations with undetermined coefficients. To achieve this, we utilized shifted Vieta-Fibonacci polynomials to construct an operational matrix of integration, where the integral operator is defined in the Riemann-Liouville sense. The solutions to second-kind VIEs and their systems are obtained numerically at the collocation points using the Tau method and using the operational matrix constructed for efficient computation.
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