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

The goal of this study is to use our suggested generalized Legendre wavelet method to solve delay and equations of neutral differential form with pro-portionate delays of different orders. Delay differential equations have some application in the mathematical and physical modelling of real-world prob-lems such as human body control and multibody control systems, electric circuits, dynamical behavior of a system in fluid mechanics, chemical en-gineering, 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, and show that the current method is quite effective in order to solve such sorts of differential equations.