Orthonormal Bernoulli Polynomials for Solving a Class of Two Dimensional Stochastic Volterra–Fredholm Integral Equations

Ahmad Pourdarvish; Khosro Sayevand; Iman Masti; Sunil Kumar

doi:10.1007/s40819-022-01246-z

Orthonormal Bernoulli Polynomials for Solving a Class of Two Dimensional Stochastic Volterra–Fredholm Integral Equations

Ahmad Pourdarvish
, Khosro Sayevand
, Iman Masti
, Sunil Kumar

Mazandaran University
Malayer University
National Institute of Technology Jamshedpur

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Analyzing the mathematical models involving Itô integral, in particular in science and engineering has received much attention, and the reason for this issue is the randomness and lack of access to the exact answer of this type of models. For this purpose, in this paper, the approximate solution of two dimensional (2-D) stochastic Volterra–Fredholm integral equations (SVFIEs) based on the operational matrix method and orthonormal Bernoulli polynomials (OBP) is investigated. Some results and convergence analysis are also presented. Finally, by presenting three examples and reviewing the results and numerical comparisons, we showed that the proposed method has an excellent performance.

Original language	English
Article number	31
Journal	International Journal of Applied and Computational Mathematics
Volume	8
Issue number	1
DOIs	https://doi.org/10.1007/s40819-022-01246-z
State	Published - Feb 2022
Externally published	Yes

Keywords

Error analysis
Itô integral
Operational matrix
Orthonormal Bernoulli polynomials
Stochastic Volterra–Fredholm integral equations

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10.1007/s40819-022-01246-z

Cite this

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title = "Orthonormal Bernoulli Polynomials for Solving a Class of Two Dimensional Stochastic Volterra–Fredholm Integral Equations",

abstract = "Analyzing the mathematical models involving It{\^o} integral, in particular in science and engineering has received much attention, and the reason for this issue is the randomness and lack of access to the exact answer of this type of models. For this purpose, in this paper, the approximate solution of two dimensional (2-D) stochastic Volterra–Fredholm integral equations (SVFIEs) based on the operational matrix method and orthonormal Bernoulli polynomials (OBP) is investigated. Some results and convergence analysis are also presented. Finally, by presenting three examples and reviewing the results and numerical comparisons, we showed that the proposed method has an excellent performance.",

keywords = "Error analysis, It{\^o} integral, Operational matrix, Orthonormal Bernoulli polynomials, Stochastic Volterra–Fredholm integral equations",

author = "Ahmad Pourdarvish and Khosro Sayevand and Iman Masti and Sunil Kumar",

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T1 - Orthonormal Bernoulli Polynomials for Solving a Class of Two Dimensional Stochastic Volterra–Fredholm Integral Equations

AU - Pourdarvish, Ahmad

AU - Sayevand, Khosro

AU - Masti, Iman

AU - Kumar, Sunil

PY - 2022/2

Y1 - 2022/2

N2 - Analyzing the mathematical models involving Itô integral, in particular in science and engineering has received much attention, and the reason for this issue is the randomness and lack of access to the exact answer of this type of models. For this purpose, in this paper, the approximate solution of two dimensional (2-D) stochastic Volterra–Fredholm integral equations (SVFIEs) based on the operational matrix method and orthonormal Bernoulli polynomials (OBP) is investigated. Some results and convergence analysis are also presented. Finally, by presenting three examples and reviewing the results and numerical comparisons, we showed that the proposed method has an excellent performance.

AB - Analyzing the mathematical models involving Itô integral, in particular in science and engineering has received much attention, and the reason for this issue is the randomness and lack of access to the exact answer of this type of models. For this purpose, in this paper, the approximate solution of two dimensional (2-D) stochastic Volterra–Fredholm integral equations (SVFIEs) based on the operational matrix method and orthonormal Bernoulli polynomials (OBP) is investigated. Some results and convergence analysis are also presented. Finally, by presenting three examples and reviewing the results and numerical comparisons, we showed that the proposed method has an excellent performance.

KW - Error analysis

KW - Itô integral

KW - Operational matrix

KW - Orthonormal Bernoulli polynomials

KW - Stochastic Volterra–Fredholm integral equations

UR - https://www.scopus.com/pages/publications/85123494838

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DO - 10.1007/s40819-022-01246-z

M3 - Article

AN - SCOPUS:85123494838

SN - 2349-5103

VL - 8

JO - International Journal of Applied and Computational Mathematics

JF - International Journal of Applied and Computational Mathematics

IS - 1

M1 - 31

ER -

Orthonormal Bernoulli Polynomials for Solving a Class of Two Dimensional Stochastic Volterra–Fredholm Integral Equations

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Keywords

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