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.
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