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Utilizing Laguerre Polynomials to Compute a Numerical Solution for the Second Kind Linear System of Volterra Integral Equations |
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PP: 1057-1069 |
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doi:10.18576/amis/200415
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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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| This paper develops a highly efficient numerical framework using Laguerre polynomials to solve systems of linear Volterra integral equations of the second kind. A primary advantage of this approach is its use of the semi-infinite interval [0,∞), which eliminates the need for the artificial domain truncation required by traditional bases like Chebyshev or block-pulse functions. This makes the method uniquely suited for accurately modeling memory-dependent processes such as damping and diffusion. By deriving a specialized operational matrix, the system is transformed into a system of linear algebraic equations. Numerical results demonstrate spectral convergence and exceptional precision, achieving results comparable to the exact solution with a minimal number of basis functions. Comparative analysis confirms that the proposed method significantly outperforms existing benchmarks in both computational efficiency and accuracy for systems with decaying exponential kernels.
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