A new scheme for solving nonlinear Stratonovich Volterra integral equations via Bernoulli's approximation. Issue 13 (3rd October 2017)

• Record Type: Journal Article
• Authors: Mirzaee, Farshid; Samadyar, Nasrin; Hoseini, Seyede Fatemeh
• Is Part Of: Applicable analysis. Volume 96:Issue 13(2017)
• Page Start: 2163
• Page End: 2179
• Publication Date: 2017-10-03
• Subjects: Stochastic operational matrix -- nonlinear Stratonovich Volterra integral equations -- Bernoulli polynomials -- error analysis; 65C30 -- 60H35 -- 60H20 -- 11B68 -- 60J65; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1208815
• Languages: English
• ISSNs: 0003-6811

Abstract

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.