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

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.

Keywords:

• Stochastic operational matrix
• nonlinear Stratonovich Volterra integral equations
• Bernoulli polynomials
• error analysis

AMS Subject Classifications:

• 65C30
• 60H35
• 60H20
• 11B68
• 60J65

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.