A numerical study on reaction-diffusion problem using radial basis functions

In this paper, the collocation approach, based on the indirect radial basis functions on boundary value problems (IRBFB), is used to obtain a solution for the problem of a non-linear model of reaction-diffusion in porous catalysis pellets for the case of $n$th-order reaction. One of the boundaries of porous slab is impermeable and the other one is held at constant concentration. We applied this method through the integration process on the boundary value reaction-diffusion problem. The Thiele modulus thus measures the relative importance of the diffusion and reaction phenomena. Interestingly, for the large Thiele modulus the IRBFB offer a reasonable solution. Numerical results and findings obtained by the comparison with finite difference method, show a good accuracy and appropriate convergence rate of IRBFB process.