Dr. Kareem T. Elgindy Publishes in Mathematics and Computers in Simulation


The Research and Postgraduate Centre congratulates Assoc. Prof. Dr. Kareem T. Elgindy from the Department of Mathematics for publishing two articles in Mathematics and Computers in Simulation, (Q1, IF: 4.6).

The first journal article titled Direct integral pseudospectraland integral spectral methods for solving a class of infinite horizon optimal output feedback control problems using rational and exponential Gegenbauer polynomials” is concerned with the numerical solution of a class of infinite-horizon linear regulation problems with state equality constraints and output feedback control. Two proposed numerical methods to convert the optimal control problem into nonlinear programming problems (NLPs) using collocations in a semi-infinite domain based on rational Gegenbauer (RG) and exponential Gegenbauer (EG) basis functions. New properties of these basis functions are introduced and their quadratures and associated truncation errors are derived. A rigorous stability analysis of the RG and EG interpolations is also presented. The effects of various parameters on the accuracy and efficiency of the proposed methods are investigated. The performance of the developed integral spectral method is demonstrated using two benchmark test problems related to a simple model of a divert control system and the lateral dynamics of an F-16 aircraft. Comparisons of the results of the current study with available numerical solutions show that the developed numerical scheme is efficient and exhibits faster convergence rates and higher accuracy.

 This article can be accessed at: https://doi.org/10.1016/j.matcom.2023.12.026

In the second journal article titled Fourier-Gegenbauer pseudospectral method for solving time-dependent one-dimensional fractional partial differential equations with variable coefficients and periodic solutions”, a novel pseudospectral (PS) method is presented for solving a new class of initial-value problems (IVPs) of time-dependent one-dimensional fractional partial differential equations (FPDEs) with variable coefficients and periodic solutions. A main ingredient is the use of the recently developed periodic RL/Caputo fractional derivative (FD) operators with sliding positive fixed memory length of Bourafa et al. (2021) or their reduced forms obtained by Elgindy (2023) as the natural FD operators to accurately model FPDEs with periodic solutions. The proposed method converts the IVP into a well-conditioned linear system of equations using the PS method based on Fourier collocations and Gegenbauer quadratures. The reduced linear system has a simple special structure and can be solved accurately and rapidly by using standard linear system solvers. A rigorous study of the computational storage requirements as well as the error and convergence of the proposed method is presented. The idea and results presented in this paper are expected to be useful in the future to address more general problems involving FPDEs with periodic solutions.

This article can be assessed at: https://doi.org/10.1016/j.matcom.2023.11.034

Dr. Kareem T. Elgindy is an Associate Professor at School of Physics and Mathematics, Xiamen University Malaysia. In 2016, Dr. Kareem was granted the title of a Visiting Scholar at California Institute of Technology (Caltech) after he received the AY2016-2017 Fulbright Egyptian Visiting Scholar Award. Later, he held the ranks of Assistant and Associate Professor in the Mathematics Department at King Fahd University of Petroleum & Minerals (KFUPM), KSA during 2017-2022. He was also a member of the Interdisciplinary Research Center for Membranes and Water Security (IRC-MWS), KFUPM, in 2022. His research interests include numerical analysis, (fractional) optimal control theory, (fractional) partial differential equations, mathematical biology, and nonlinear programming.

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