The Effect of Radial Basis Functions (RBFs) Method in Solving Coupled Lane-Emden Boundary Value Problems in Catalytic Diffusion Reactions

In this paper, the radial basis functions (RBFs) method is applied to solve the coupled Lane-Emden boundary value problems arising in catalytic diffusion reactions. First, we multiply the equations by x to overcome the difficulties of the singularity at the origin. Then, the Kansa collocation method based on radial basis functions is used to approximate the unknown functions. By this technique, the problem with boundary conditions is reduced to a system of algebraic equations. We solve this system and compare the maximal residual error with the results previously, which show the presented method is efficient and produces very accurate and rapidly convergent numerical results in considerably low computational effort and easy implementation.