Available online at www.ispacs.com/cna Volume 2011, Year 2011 Article ID cna-00104, 11 pages doi: 10.5899/2011/cna-00104 Research Article A numerical study on reaction–diffusion problem using radial basis functions K. Parand a, ∗ , S. Kazem b , A.R. Rezaei a (a) Department of Computer Sciences, Shahid Beheshti University, G.C., Tehran, Iran (b) Department of Mathematics, Imam Khomeini International University, Ghazvin, Iran Copyright 2011 c ⃝ K. Parand, S. Kazem and A.R. Rezaei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract 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 nth–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 ap- propriate convergence rate of IRBFB process. Keywords : Collocation method; Non-linear ODE; Radial Basis Functions; Multiquadric; Reaction- diffusion. 1 Introduction One of the old, yet significant, non-linear problems in chemical engineering is related to the model of coupled diffusion and the reaction in porous catalysis pellets. Thiele in [26] found the analytical solution for the first–order reaction in 1939. Later, Wheeler in [27], Aris in [3] et al., referred to this problem in detail in their studies. However, most of their conclusions were based on the first–order reaction. Other researchers, such as Satterfild in [23], have considered the nth-order reactions; however, they were unable to * Corresponding author. Email address: k parand@sbu.ac.ir Tel: +989124893213 1