This article gives an effective strategy to solve nonlinear stochastic Itô-Volterra integral equations (NSIVIE). These equations can be reduced to a system of nonlinear algebraic equations with unknown coefficients, using Bernoulli wavelets, their operational matrix of integration (OMI), stochastic operational matrix of integration (SOMI) and these equations can be solved numerically. Error analysis of the proposed method is given. Moreover, the results obtained are compared to exact solutions with numerical examples to show that the method described is accurate and precise.
This article gives an effective strategy to solve the system of linear Stratonovich Volterra integral equations. Using the Bernstein polynomial multiwavelets operational matrix of integration and its stochastic operational matrix of integration, the system of linear Stratonovich Volterra integral equations can be reduced to a system of linear algebraic equations with unknown coefficients, and the obtained linear algebraic equations are solved numerically. Error analysis of the proposed method is given. Numerical examples are presented to show that the method described is accurate and precise. Keywords-Bernstein polynomials, Bernstein polynomial multiwavelets, Brownian motion, Stratonovich Volterra integral equations, Stochastic operational matrix of integration of Bernstein polynomial multiwavelets.
In this paper, the CAS wavelets stochastic operational matrix method is developed for the numerical solution of stochastic integral equations. Properties of CAS wavelets and its function approximation are discussed. Firstly, the CAS wavelets stochastic operational matrix of integration is generated. This stochastic operational matrix is employed for solving stochastic integral equations. Next, this technique converts the stochastic integral equation into system of algebraic equations and then solving these equations we obtain the CAS wavelet coefficients. The accuracy of the proposed method is justified through the Illustrative example and the obtained solutions are compared with those of exact solutions. Error analysis is presented to show the efficiency of the proposed method.
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