1. A numerical method for solving -dimensional stochastic Itô–Volterra integral equations by stochastic operational matrix
- Author
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Maleknejad, K., Khodabin, M., and Rostami, M.
- Subjects
- *
NUMERICAL analysis , *DIMENSIONAL analysis , *STOCHASTIC analysis , *INTEGRAL equations , *VOLTERRA equations , *MATHEMATICAL models , *APPROXIMATION theory - Abstract
Abstract: The multidimensional Itô–Volterra integral equations arise in many problems such as an exponential population growth model with several independent white noise sources. In this paper, we obtain a stochastic operational matrix of block pulse functions on interval to solve m-dimensional stochastic Itô–Volterra integral equations. By using block pulse functions and their stochastic operational matrix of integration, -dimensional stochastic Itô–Volterra integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. We prove that the rate of convergence is . Furthermore, a 95% confidence interval of the errors’ mean is made, the results shows that the approximate solutions have a credible degree of accuracy. [Copyright &y& Elsevier]
- Published
- 2012
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