Advances and Applications in Statistics
Volume 48, Issue 5, Pages 317 - 336
(May 2016) http://dx.doi.org/10.17654/AS048050317 |
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NUMERICAL SOLUTION OF STOCHASTIC NONLINEAR VOLTERRA INTEGRAL EQUATIONS BY A STOCHASTIC OPERATIONAL MATRIX BASED ON HAAR WAVELETS
B. Farahani, M. Khodabin and R. Ezzati
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Abstract: In this paper, an effective method to solve stochastic nonlinear Volterra integral equations (SNVIE) is proposed. This method is based on the Haar wavelets (HW) and their stochastic operational matrix of integration. By applying this method, the SNVIE is reduced to a nonlinear upper triangular system, which can be solved by using known numerical methods as Newton method. Furthermore, the error analysis is done for this method. Finally, to illustrate the efficiency of this scheme, some examples are given. |
Keywords and phrases: Haar wavelets, stochastic operational matrix, stochastic nonlinear Volterra integral equations, Brownian motion. |
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