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...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 43; no. 8; pp. 5212 - 5233
Main Authors: Saffarzadeh, Masoud, Heydari, Mohammad, Barid Loghmani, Ghasem
Format: Journal Article
Language:English
Published: Freiburg Wiley Subscription Services, Inc 30.05.2020
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6261