Mahnaz Asgari, Elham Hashemizadeh, Morteza Khodabin and Khosrow Maleknejad: Numerical solution of nonlinear stochastic integral equation by stochastic operational matrix based on Bernstein polynomials, p.3-12

Abstract:

In this paper, a practical and computational numerical method based on Bernstein polynomials for solving nonlinear stochastic integral equations is presented. Stochastic operational matrix of Bernstein polynomials is determined. The main idea is that it reduces the stochastic integral equation to a system of algebraic equations. Thus we can solve the problem by iteration methods. Numerical example illustrates the efficiency and accuracy of the method.

Key Words: Bernstein polynomial; Brownian motion; Itô integral; Stochastic operational matrix; Nonlinear stochastic integral equation.

2000 Mathematics Subject Classification: Primary: 65C30;
Secondary: 60H35, 65C20, 60H20, 68U20.

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