An Application of Wavelet Method for Solving Coupled Boundary Value Problems: Catalytic Diffusion Reactions

In this study, Hermite wavelets are employed to solve coupled Lane–Emden boundary value problems that arise in catalytic diffusion processes. These problems are mathematically challenging due to their singular behavior at the origin, which is resolved by reformulating them into an equivalent coupled system. Unlike traditional semi-analytical techniques such as the Adomian Decomposition Method (ADM) or the Homotopy Analysis Method (HAM), the Hermite wavelet approach avoids the use of auxiliary or convergence-control parameters, offering a more direct and reliable computational framework. Numerical investigations demonstrate the efficiency of the proposed method, achieving maximum absolute errors of order [Formula: see text] and residual errors consistently below [Formula: see text], thereby confirming an approximately exponential convergence rate. When compared with ADM, HAM, and other recent approaches reported in the literature, the Hermite wavelet method shows superior accuracy and faster convergence, highlighting its potential as a powerful tool for addressing nonlinear singular models in catalytic diffusion and related applications.