Sinc methods involving exponential transformations to solve Lane–Emden type equations

摘要

We study the performance of the sinc methods based on single and double exponential transformations, for numerical solution of Lane–Emden type equations. the sinc-Galerkin and collocation methods based on single and double exponential transformations developed and for comparison, these methods are applied to three examples. By considering the maximum absolute errors in the solutions and tabulated in table, we conclude that the sinc methods based on DE transformation converges to the exact solution rapidly, with order O(exp (?cN/ log N)) accuracy in comparison with the sinc methods based on SE transformation, with order O(exp (?c√N)) accuracy, where c is independent of N and N is a parameter representing the number of terms in the sinc approximation.