Bernstein Series Solution of a Class of Lane-Emden Type Equations

摘要

The purpose of this study is to present an approximate solution that depends on collocation points and Bernstein polynomials for a class of Lane-Emden type equations with mixed conditions. The method is given with some priori error estimate. Even the exact solution is unknown, an upper bound based on the regularity of the exact solution will be obtained. By using the residual correction procedure, the absolute error can be estimated. Also, one can specify the optimal truncation limit n which gives a better result in any norm. Finally, the effectiveness of the method is illustrated by some numerical experiments. Numerical results are consistent with the theoretical results.