Taha M. El-Gindy

Bio: Taha M. El-Gindy is an academic researcher from Assiut University. The author has contributed to research in topics: Chebyshev equation & Chebyshev iteration. The author has an hindex of 3, co-authored 5 publications receiving 65 citations.

A New Image Encryption Algorithm for Grey and Color Medical Images

Abstract: Recently, diagnosing diseases using medical images became crucial. As these images are transmitted through the network, they need a high level of protection. If the data in these images are liable for unauthorized usage, this may lead to severe problems. There are different methods for securing images. One of the most efficient techniques for securing medical images is encryption. Confusion and diffusion are the two main steps used in encryption algorithms. This paper presents a new encryption algorithm for encrypting both grey and color medical images. A new image splitting technique based on image blocks introduced. Then, the image blocks scrambled using a zigzag pattern, rotation, and random permutation. Then, a chaotic logistic map generates a key to diffuse the scrambled image. The efficiency of our proposed method in encrypting medical images is evaluated using security analysis and time complexity. The security is tested in entropy, histogram differential attacks, correlation coefficient, PSNR, keyspace, and sensitivity. The achieved results show a high-performance security level reached by successful encryption of both grey and color medical images. A comparison with various encryption methods is performed. The proposed encryption algorithm outperformed the recent existing encryption methods in encrypting medical images.

A Chebyshev approximation for solving optimal control problems

Abstract: This paper presents a numerical solution for solving optimal control problems, and the controlled Duffing oscillator. A new Chebyshev spectral procedure is introduced. Control variables and state variables are approximated by Chebyshev series. Then the system dynamics is transformed into systems of algebraic equations. The optimal control problem is reduced to a constrained optimization problem. Results and comparisons are given at the end of the paper.

An optimization technique for the falkner-skan equation

Abstract: Rayleigh-Ritz method is modified to use an unconstrained optimization method in its minimization process. Chebyshev spectral technique based on El-Gendi method is used to approximate the solution of the problem and its derivatives. The Falkner-Skan equation has been solved through the use of Chebyshev Spectral-Ritz method for different values of its parameters. Comparisons are made between the proposed method and the classical solution.

Effective numerical technique for solving variable order integro-differential equations

Abstract: In this article, an effective numerical technique for solving the variable order Fredholm–Volterra integro-differential equations (VO-FV-IDEs), systems of VO-FV-IDEs and variable order Volterra partial integro-differential equations (VO-V-PIDEs) is given. The suggested technique is built on the combination of the spectral collocation method with some types of operational matrices of the variable order fractional differentiation and integration of the shifted fractional Gegenbauer polynomials (SFGPs). The proposed technique reduces the considered problems to systems of algebraic equations that are straightforward to solve. The error bound estimation of using SFGPs is discussed. Finally, the suggested technique’s authenticity and efficacy are tested via presenting several numerical applications. Comparisons between the outcomes achieved by implementing the proposed method with other numerical methods in the existing literature are held, the obtained numerical results of these applications reveal the high precision and performance of the proposed method.