A numerical computation for solving delay and neutral differential equations based on a new modification to the Legendre wavelet method

Articles in Press

Document Type : Research Article

Authors

• Naglaa M. El-Shazly
• Mohamed A. Ramadan

Mathematics and Computer ScienceDepartment, Faculty of Science, Menoufia University, Egypt

10.22067/ijnao.2024.87373.1412

Abstract

The goal of this study is to use our suggested generalized Legendre wavelet method (GLWM ) [1] to solve delay and equations of neutral differential form with proportionate delays of different orders. Delay differential equations (DDEs) have some application in the mathematical and physical modeling of real-world problems such as human body control and multibody control systems, electric circuits, the dynamical behavior of a system in fluid mechanics, chemical engineering, infectious diseases, bacteriophage infection’s spread, population dynamics, epidemiology, physiology, immunology, and neural networks.
The use of orthonormal polynomials is the key advantage of this method because it reduces computational cost and runtime. Some examples are provided to demonstrate the effectiveness and accuracy of the suggested strategy. The method's accuracy is reported in terms of absolute errors. The numerical findings are compared to other numerical approaches in the literature, particularly the regular Legendre wavelets method (RLWM ), and show that the current method is quite effective in solving such sorts of differential equations

Keywords

• Generalized Legendre wavelets
• Orthonormal polynomials delay differential equations
• Neutral differential equations, Accuracy

Main Subjects

• Numerical Analysis

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