NUMERICAL SOLUTION OF A NONLINEAR BOUNDARY VALUE PROBLEM IN CATALYST PORES USING FINITE DIFFERENCE METHOD AND MATLAB FSOLVE

Abstract This study presents a robust numerical framework for solving nonlinear boundary value problems (BVPs) in catalytic pores by combining the finite difference method (FDM) with MATLAB’s fsolve solver. The governing nonlinear diffusion–reaction equation is discretized using central finite differences, and the resulting system of nonlinear algebraic equations is iteratively solved with fsolve. Concentration profiles were investigated across a wide range of Thiele modulus values and reaction orders, and the predictions were compared against analytical solutions available in the literature. The results demonstrate excellent agreement with analytical benchmarks, confirming the accuracy and stability of the proposed approach. For zeroth-order kinetics, reactant depletion occurs rapidly at relatively low Thiele modulus values, whereas first-order kinetics require significantly higher Thiele modulus values for complete consumption. These findings highlight the dominant role of pore-scale transport limitations in catalyst performance. Beyond validation, the methodology provides a flexible computational platform that can be readily extended to more complex scenarios, including variable diffusivities, multidimensional geometries, and higher-order reaction mechanisms. The integration of FDM with iterative solvers such as fsolve thus offers an adaptable and efficient tool for advancing catalyst design and optimization in heterogeneous reaction engineering.