SEMI-ANALYTIC FIBONACCI POLYNOMIAL SOLUTION FOR VOLTERRA–FREDHOLM INTEGRAL EQUATION WITH ERROR ANALYSIS

Mahmoud M. Mokhtar, M. H. El Dewaik and Amany S. Mohamed
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Mahmoud M. Mokhtar: Department of Basic Science, Faculty of Engineering, Modern University for Technology and Information (MTI), Egypt
M. H. El Dewaik: Department of Basic Science, The British University in Egypt, El-Shorouk City, Cairo, Egypt
Amany S. Mohamed: Department of Mathematics, Faculty of Science, Helwan University, Egypt

FRACTALS (fractals), 2022, vol. 30, issue 08, 1-10

Abstract: Herein, a spectral scheme is implemented and analyzed for numerically handling general Volterra–Fredholm integral equations (VFIEs), for this purpose, the linearly independent Fibonacci polynomials are utilized as basis functions for the solution, then the spectral collocation process is used to transform the integral equation into a system of algebraic equations with undetermined coefficients. The error, convergence and stability analyses of the scheme are discussed in-depth, some numerical examples are exhibited to ensure the applicability, efficiency and accuracy of the solver.

Keywords: Fibonacci Polynomials; Volterra–Fredholm Integral Equation; Tau Method; Error Analysis (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402307

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