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Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 13
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Articles

A new scheme for solving nonlinear Stratonovich Volterra integral equations via Bernoulli’s approximation

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Pages 2163-2179 | Received 25 Mar 2016, Accepted 29 Jun 2016, Published online: 18 Jul 2016
 

Abstract

In this paper, an efficient method for solving nonlinear Stratonovich Volterra integral equations is proposed. By using Bernoulli polynomials and their stochastic operational matrix of integration, these equations can be reduced to the system of nonlinear algebraic equations with unknown Bernoulli coefficient which can be solved by numerical methods such as Newton’s method. Also, an error analysis is valid under fairly restrictive conditions. Furthermore, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient than the block pulse functions method.

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Acknowledgements

We would like to thank the editor and the anonymous referees for their comments which considerably improved the paper.

Notes

No potential conflict of interest was reported by the authors.

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