Numerical solution of stochastic Volterra integral equations by a stochastic operational matrix based on block pulse functions (original) (raw)
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A new computational method based on Haar wavelets is proposed for solving multidimensional stochastic Itô-Volterra integral equations. The block pulse functions and their relations to Haar wavelets are employed to derive a general procedure for forming stochastic operational matrix of Haar wavelets. Then, Haar wavelets basis along with their stochastic operational matrix are used to approximate solution of multidimensional stochastic Itô-Volterra integral equations. Convergenc and error analysis of the proposed method are discussed. In order to show the effectiveness of the proposed method, it is applied to some problems.
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International Journal of Dynamical Systems and Differential Equations, 2021
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Numerical Approximation of Stochastic Volterra Integral Equation Using Walsh Function
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