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Original Articles

An improved reproducing kernel method for Fredholm integro-differential type two-point boundary value problems

, , &
Pages 1015-1023 | Received 20 Jan 2017, Accepted 18 Mar 2017, Published online: 10 May 2017
 

ABSTRACT

In this work, an improved reproducing kernel method to find the numerical solution of Fredholm integro-differential equation type boundary value problems has been developed. Based on the good properties of reproducing kernel function and the conjugate operator, the solution representation is obtained. Meanwhile, we prove that the approximation converges to the exact solution uniformly. After that the convergence estimates are derived.

2000 AMS CLASSIFICATIONS:

Acknowledgements

The authors would like to express their thanks to unknown referees for the careful reading of the manuscript and helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work were supported by the Youth Foundation of Heilongjiang Province [Grant No.JJ2016QN0211] and TianYuan Special Funds of the National Natural Science Foundation of China [Grant No.11426079] and National Natural Science Funds of China [Grant No.11401145] and Science Research Foundation of Heilongjiang Province [Grant No. A201411].

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