A new robust line search technique based on Chebyshev polynomials. - Kareem T. Elgindy; Abdel-Rahman Hedar (Appl. Math. Comput., 2008)

Generation of higher order pseudospectral integration matrices. - Kareem T. Elgindy (Appl. Math. Comput., 2009)

On the optimization of Gegenbauer operational matrix of integration. - Kareem T. Elgindy; Kate Smith-Miles (Adv. Comput. Math., 2013)

Optimal Gegenbauer quadrature over arbitrary integration nodes. - Kareem T. Elgindy; Kate Amanda Smith-Miles (J. Comput. Appl. Math., 2013)

Fast, accurate, and small-scale direct trajectory optimization using a Gegenbauer transcription method. - Kareem T. Elgindy; Kate Amanda Smith-Miles (J. Comput. Appl. Math., 2013)

Solving boundary value problems, integral, and integro-differential equations using Gegenbauer integration matrices. - Kareem T. Elgindy; Kate Smith-Miles (J. Comput. Appl. Math., 2013)

High-order integral nodal discontinuous Gegenbauer-Galerkin method for solving viscous Burgers' equation. - Kareem T. Elgindy; Bülent Karasözen (Int. J. Comput. Math., 2019)

A high-order embedded domain method combining a Predictor-Corrector-Fourier-Continuation-Gram method with an integral Fourier pseudospectral collocation method for solving linear partial differential equations in complex domains. - Kareem T. Elgindy (J. Comput. Appl. Math., 2019)

High-order Gegenbauer integral spectral element method integrated with an adaptive Chebyshev optimization strategy for solving linear singularly perturbed differential equations. - Kareem T. Elgindy; Hareth M. Refat (J. Comput. Appl. Math., 2020)

New Optimal Periodic Control Policy for the Optimal Periodic Performance of a Chemostat Using a Fourier-Gegenbauer-Based Predictor-Corrector Method. - Kareem T. Elgindy (CoRR, 2022)

A Direct Integral Pseudospectral Method for Solving a Class of Infinite-Horizon Optimal Control Problems Using Gegenbauer Polynomials and Certain Parametric Maps. - Kareem T. Elgindy; Hareth M. Refat (CoRR, 2022)

High-order numerical solution of viscous Burgers' equation using an extended Cole-Hopf barycentric Gegenbauer integral pseudospectral method. - Sayed A. Dahy; Kareem T. Elgindy (Int. J. Comput. Math., 2022)

Fourier-Gegenbauer Pseudospectral Method for Solving Periodic Higher-Order Fractional Optimal Control Problems. - Kareem T. Elgindy (CoRR, 2023)

Fourier-Gegenbauer pseudospectral method for solving periodic fractional optimal control problems. - Kareem T. Elgindy (Math. Comput. Simul., 2024)

Direct integral pseudospectral and integral spectral methods for solving a class of infinite horizon optimal output feedback control problems using rational and exponential Gegenbauer polynomials. - Kareem T. Elgindy; Hareth M. Refat (Math. Comput. Simul., 2024)

Fourier-Gegenbauer pseudospectral method for solving time-dependent one-dimensional fractional partial differential equations with variable coefficients and periodic solutions. - Kareem T. Elgindy (Math. Comput. Simul., 2024)

Fourier-Gegenbauer Integral-Galerkin Method for Solving the Advection-Diffusion Equation With Periodic Boundary Conditions. - Kareem T. Elgindy (CoRR, 2025)

The Numerical Approximation of Caputo Fractional Derivative of Higher Orders Using A Shifted Gegenbauer Pseudospectral Method: Two-Point Boundary Value Problems of the Bagley Torvik Type Case Study. - Kareem T. Elgindy (CoRR, 2025)

Super-Exponential Approximation of the Riemann-Liouville Fractional Integral via Shifted Gegenbauer Pseudospectral Methods. - Kareem T. Elgindy (CoRR, 2025)

Hybrid Shifted Gegenbauer Integral-Pseudospectral Method for Solving Time-Fractional Benjamin-Bona-Mahony-Burgers Equation. - Kareem T. Elgindy (CoRR, 2025)

Optimal Periodic Control of Unmanned Aerial Vehicles Based on Fourier Integral Pseudospectral and Edge-Detection Methods. - Kareem T. Elgindy (Unmanned Syst., 2025)