2,023 research outputs found
An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method
In this paper we propose a collocation method for solving some well-known
classes of Lane-Emden type equations which are nonlinear ordinary differential
equations on the semi-infinite domain. They are categorized as singular initial
value problems. The proposed approach is based on a Hermite function
collocation (HFC) method. To illustrate the reliability of the method, some
special cases of the equations are solved as test examples. The new method
reduces the solution of a problem to the solution of a system of algebraic
equations. Hermite functions have prefect properties that make them useful to
achieve this goal. We compare the present work with some well-known results and
show that the new method is efficient and applicable.Comment: 34 pages, 13 figures, Published in "Computer Physics Communications
Optimal Perturbation Iteration Method for Bratu-Type Problems
In this paper, we introduce the new optimal perturbation iteration method
based on the perturbation iteration algorithms for the approximate solutions of
nonlinear differential equations of many types. The proposed method is
illustrated by studying Bratu-type equations. Our results show that only a few
terms are required to obtain an approximate solution which is more accurate and
efficient than many other methods in the literature.Comment: 11 pages, 3 Figure
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