Convergence analysis of an iterative algorithm to solve system of nonlinear stochastic Itô‐Volterra integral equations

In this paper, an efficient and accurate numerical iterative algorithm based on the linear spline interpolation for solving the system of nonlinear stochastic Itô‐Volterra integral equations is presented. The most important merit of this method is that it does not need to solve any system of nonline...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Mathematical methods in the applied sciences Ročník 43; číslo 8; s. 5212 - 5233
Hlavní autoři: Saffarzadeh, Masoud, Heydari, Mohammad, Barid Loghmani, Ghasem
Médium: Journal Article
Jazyk:angličtina
Vydáno: Freiburg Wiley Subscription Services, Inc 30.05.2020
Témata:
Convergence
Integral equations
Interpolation
Iterative algorithms
Iterative methods
linear spline interpolation
Mathematical analysis
multiple stock models
Nonlinear equations
pendulum problem
predator‐prey models
successive approximations method
system of stochastic Volterra integral equations
Upper bounds
Volterra integral equations
ISSN:0170-4214, 1099-1476
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:In this paper, an efficient and accurate numerical iterative algorithm based on the linear spline interpolation for solving the system of nonlinear stochastic Itô‐Volterra integral equations is presented. The most important merit of this method is that it does not need to solve any system of nonlinear algebraic equations. An upper bound for the linear spline approximation of the stochastic function is provided. Using this upper bound and under the Lipschitz and linear growth conditions, the convergence analysis of the suggested method is studied. Finally, to verify the efficiency of the proposed scheme, some problems in the finance, physics, and biology are investigated, and the obtained results are compared with the stochastic θ‐method.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6261