Numerical method for a class of singular non-linear boundary value problems using Green's functions

Abstract

A numerical method based on Green's function is presented for solving a class of singular non-linear boundary value problems. By applying Green's function an equivalent integral equation, which can be solved by linear interpolation on a non-uniform mesh, can be derived from the singular non-linear boundary value problem. This equation is shown to be second-order convergent. The numerical method can be extended to more general singular boundary value problems. Numerical experiments support these theoretical results and indicate that the estimates are sharp.

Keywords:

• Singular equations
• Boundary value problems
• Green's function
• Convergence

Acknowledgements

The author would like to thank the anonymous referees for their valuable comments. The work was supported by the National Natural Science Foundation (Grant No. 10671180,10471129) of China and Research Project (20060182) of the Department of Education, Zhejiang Province, China.

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Notes on contributors

Zhongdi Cen

Email: [email protected]