Advances in Differential Equations and Control Processes
Volume 17, Issue 3, Pages 189 - 212
(August 2016) http://dx.doi.org/10.17654/DE017030189 |
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NUMERICAL SOLUTION OF m-DIMENSIONAL STOCHASTIC ITÔ-VOLTERRA INTEGRAL EQUATIONS BY STOCHASTIC OPERATIONAL MATRIX BASED ON RATIONALIZED HAAR WAVELET
M. Khodabin and M. Rostami
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Abstract: The multidimensional Itô-Volterra integral equations arise in many problems such as exponential population growth model with several independent white noise sources. In this paper, we obtain stochastic operational matrix of rationalized Haar functions on interval to solve m-dimensional stochastic Itô-Volterra integral equations. By using rationalized Haar functions and their stochastic operational matrix of integration, m-dimensional stochastic Itô-Volterra integral equation can be reduced to a linear system which can be directly solved by Gaussian elimination method. This scheme is applied for some numerical examples in the population growth. The results show the efficiency and accuracy of the method. |
Keywords and phrases: rationalized Haar functions, stochastic operational matrix, product matrix, stochastic Itô-Volterra integral equations, Itô integral, Brownian motion process. |
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