Abstract
This paper investigates the numerical solution of two-dimensional nonlinear stochastic Ito-Volterra integral equations based on block pulse functions. The nonlinear stochastic integral equation is transformed into a set of algebraic equations by operational matrix of block pulse functions. Then, we give error analysis and prove that the rate of convergence of this method is efficient. Lastly, a numerical example is given to confirm the method.
Highlights
Two-dimensional stochastic Itô-Volterra integral equations arise from many phenomena in physics and engineering fields [1]
This paper investigates the numerical solution of two-dimensional nonlinear stochastic Itô-Volterra integral equations based on block pulse functions
Fallahpour et al [7] obtained a numerical method for two-dimensional linear stochastic Volterra integral equations by block pulse functions
Summary
Two-dimensional stochastic Itô-Volterra integral equations arise from many phenomena in physics and engineering fields [1]. Fallahpour et al [3] introduced the following two-dimensional linear stochastic Volterra integral equation by Haar wavelet x= (t1,t2 ). Fallahpour et al [7] obtained a numerical method for two-dimensional linear stochastic Volterra integral equations by block pulse functions. Nemati et al [6] used two-dimensional block pulse functions and Legendre polynomials to solve those respectively Both Babolian et al [2] and Maleknejad et al [9] employed triangular functions to get the numerical solutions. As far as we known, there are hardly any papers about the numerical solution of two-dimensional nonlinear stochastic Itô-Volterra integral equations. Inspired by the above literatures, we introduce an efficient numerical method for the following nonlinear stochastic integral equation based on block pulse functions.
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