Weighted Residual Approximations of the System of Lane Emden Equations

Weighted residual approximations are numerical techniques used to model chemical reaction systems, particularly when solving complex reaction-diffusion equations. This method approximate the solution by assuming a trial function and minimizing the residual (error) introduced when substituting the trial solution into the governing equations. Using weighted functions, methods like Galerkin, Collocation, or least squares ensure the residual is minimized over the domain. These approaches are especially useful in studying reaction kinetics, transport phenomena, and coupled systems, providing an efficient way to approximate solutions where analytic solutions are difficult or impossible