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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.
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].