New cubic B-spline approximation for solving third order Emden–Flower type equations

摘要

In this article, the typical cubic B-spline collocation method equipped with new approximations for second and third order derivatives is employed to explore the numerical solution of a class of third order non-linear singular boundary value problems. The singularity is removed by means of L’Hospital’s Rule. The Taylor’s series expansion of the error term reveals that our new scheme is fifth order accurate. The proposed technique is tested on several third order Emden–Flower type equations and the numerical results are compared with those found in the current literature. It is found that our new approximation technique performs superior to the existing methods due to its simple implementation, straight forward interpolation and very less computational cost.