Computer programming-based numerical algorithm under Laguerre wavelets operational matrix of integration to the nonlinear Murray equation

In this study, I present a rapid numerical strategy based on computer programming to solve Murray's well-known nonlinear partial differential equation (PDE). This strategy utilizes the operational matrix of integration of the Laguerre wavelet. By employing the collocation approach, I transform the problem into a set of solvable nonlinear equations, considering various boundary conditions. I employ MATLAB software for solving these equations and determining the wavelet coefficients. The results obtained from the proposed method are juxtaposed with those of other existing methods using figures and tables to assess the accuracy of the proposed approach. My results demonstrate that Y approach surpasses the Haar wavelet method both in accuracy and computational efficiency across a range of scenarios. Additionally, I provide numerous theorems illustrating the uniform convergence of the Laguerre wavelet expansion of a function to itself.