Abstract
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.
Highlights
Wavelets are mathematical functions that isolate the data and analyze each variable with the corresponding resolution in various frequency components
The operational matrix method using Bernoulli wavelets for solving linear ItôVolterra integral equations was recently employed by Mirzaee and Samadyar [25]
Equation (1) is numerically solved by the use of operational matrix of integration (OMI) and stochastic OMI based on Bernoulli wavelets
Summary
Wavelets are mathematical functions that isolate the data and analyze each variable with the corresponding resolution in various frequency components. The operational matrix method using Bernoulli wavelets for solving linear ItôVolterra integral equations was recently employed by Mirzaee and Samadyar [25]. Equation (1) appears in various fields including engineering, mathematics, biology, health and social science It is very hard or even difficult to solve this equation, so we develop an efficient method for solving it. Equation (1) is numerically solved by the use of operational matrix of integration (OMI) and stochastic OMI based on Bernoulli wavelets. This equation is reduced to a nonlinear system of algebraic equations by the use of collocation points and these matrices can be solved by an effective numerical method such as Newton’s method.
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