Premium
Convergence analysis of an iterative algorithm to solve system of nonlinear stochastic Itô‐Volterra integral equations
Author(s) -
Saffarzadeh Masoud,
Heydari Mohammad,
Barid Loghmani Ghasem
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6261
Subject(s) - mathematics , nonlinear system , convergence (economics) , upper and lower bounds , volterra integral equation , lipschitz continuity , algebraic equation , spline (mechanical) , iterative method , integral equation , mathematical optimization , mathematical analysis , physics , quantum mechanics , economics , economic growth , structural engineering , engineering
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.