TY - JOUR AU - Abo-Eldahab, E. M. AU - Mohamed, A. S. AU - Ali, S. M. PY - 2022/07/14 Y2 - 2024/03/29 TI - Spectral Collocation Algorithm for Solving Fractional Volterra-Fredholm Integro-Differential Equations via Generalized Fibonacci Polynomials JF - Contemporary Mathematics JA - Contemp. Math. VL - 3 IS - 3 SE - Research Article DO - 10.37256/cm.3320221489 UR - https://ojs.wiserpub.com/index.php/CM/article/view/1489 SP - 308-325 AB - <p>In this research article, we build and implement an efficient spectral algorithm for handling linear/nonlinear mixed Volterra-Fredholm integro-differential equations. First, we expand the exact solution as a truncated series of the generalized Fibonacci polynomials, and then we discretize the equation via Simpson's quadrature formula. Finally, we collocate the resulted residual at the roots of the shifted first-kind Chebyshev polynomials. Also, the rate of convergence is studied and the truncation error estimate is reported. Some numerical examples are exhibited to prove the applicability and accuracy of the algorithm.</p> ER -