A new numerical scheme for third-order singularly Emden–Fowler equations using quintic B-spline function

Abstract

In this paper, we investigate a numerical scheme for the singular Emden–Fowler problem using quintic B-spline. We eliminate the singularity of the problem according to Lopita's law and obtain a new high-precision solution through a linear combination of the original solutions. We theoretically analyse the stability, truncation errors and convergence of the scheme and also verify it through several numerical experiments. We also provide some numerical examples to prove the efficiency of this numerical scheme and compare it with some earlier work done.

Keywords:

• Singular Emden–Fowler problem
• quintic B-spline
• error analysis
• stability
• convergence

2010 Mathematics Subject Classifications:

• 65M22
• 65M70

Acknowledgements

The authors would like to thank the editor and the reviewers for their valuable comments and suggestions to improve the results of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).