Numerical solution of stochastic Itô-Volterra integral equations based on Bernstein multi-scaling polynomials

In this paper, first, Bernstein multi-scaling polynomials (BMSPs) and their properties are introduced. These polynomials are obtained by compressing Bernstein polynomials (BPs) under sub-intervals. Then, by using these polynomials, stochastic operational matrices of integration are generated. Moreov...

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Bibliographic Details
Published in:Applied Mathematics-A Journal of Chinese Universities 2021-09, Vol.36 (3), p.317-329
Main Authors: Yaghoobnia, A. R., Khodabin, M., Ezzati, R.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Approximation
Integral equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Polynomials
Volterra integral equations
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Summary:In this paper, first, Bernstein multi-scaling polynomials (BMSPs) and their properties are introduced. These polynomials are obtained by compressing Bernstein polynomials (BPs) under sub-intervals. Then, by using these polynomials, stochastic operational matrices of integration are generated. Moreover, by transforming the stochastic integral equation to a system of algebraic equations and solving this system using Newton’s method, the approximate solution of the stochastic It ô -Volterra integral equation is obtained. To illustrate the efficiency and accuracy of the proposed method, some examples are presented and the results are compared with other methods.
ISSN:1005-1031
1993-0445
DOI:10.1007/s11766-021-3694-9