A Spectral Tau Method Based on Lucas Polynomial Approximation for Solving the Nonlinear Fractional Riccati Equation

Youssri, Youssri Hassan; Atta, Ahmed Gamal

doi:10.22034/cmde.2025.67681.3237

A Spectral Tau Method Based on Lucas Polynomial Approximation for Solving the Nonlinear Fractional Riccati Equation

Articles in Press

Document Type : Research Paper

Authors

¹ Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt.

² Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt.

10.22034/cmde.2025.67681.3237

Abstract

The nonlinear fractional Riccati equation (NFRE) can be solved using a unique spectral tau approach in this study that uses Lucas polynomials as basis functions. The fractional Caputo derivative and nonlinear terms can be handled effectively by explicit operational formulations when the Lucas basis is used. A tau projection is used to convert the problem into a nonlinear algebraic system, which is then solved by Gaussian elimination. The correctness and quick convergence of the suggested method are shown by a number of numerical tests that are backed by error analysis.

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