Iranian Journal of Mathematical Chemistry

Iranian Journal of Mathematical Chemistry

‎The effect of radial basis functions (RBFs) method in solving coupled Lane–Emden boundary value problems in‎ ‎Catalytic Diffusion Reactions

Document Type : Research Paper

Authors
Ashraf Hajiollow
Fatemeh Zabihi
Department of Applied Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎University of Kashan‎, ‎Kashan‎, ‎87317-53153‎, ‎Iran.
10.22052/ijmc.2021.242232.1561
Abstract
‎‎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.
Keywords
Coupled Lane–Emden equations‎
‎Boundary value problems‎
‎Meshless methods‎
‎Radial basis functions‎
‎Residual error

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Iranian Journal of Mathematical Chemistry
Volume 12, Issue 4
Autumn 2021
Pages 239-261