Spectral Poly-Sinc Collocation Method for Solving a Singular Nonlinear BVP of Reaction-Diffusion with Michaelis-Menten Kinetics in a Catalyst/Biocatalyst

Document Type : Research Paper


Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran


In this paper we revisit a nonlinear singular boundary value problem (SBVP) which arises frequently in mathematical model of diffusion and reaction in porous catalysts or biocatalyst pellets. A new simple variant of sinc methods so-called poly-sinc collocation method, is presented to solve non-isothermal reaction-diffusion model equation in a spherical catalyst and reaction-diffusion model equation in an electroactive polymer film. This method reduces each problem into a system of nonlinear algebraic equations, and on solving them by Newton's iteration method, we obtain the approximate solution. Through testing with numerical examples, it is found that our technique has exponentially decaying error property and performs well near singularity like other conventional sinc methods. The obtained results are in good agreement with previously reported results in the literature, and there is an impressive degree of agreement between our results and those obtained by a MAPLE ODE solver. Furthermore, the high accuracy of method is verified by using a residual evaluation strategy.


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