Numerical solution of stochastic Itô-Volterra integral equations based on Bernstein multi-scaling polynomials

The aim of this article is to propose the Lerch operational matrix method to solve a stochastic fractional differential equation. In this approach, the Lerch polynomials have been used as a basis function. Then, the product operational matrix, integral operational matrix, stochastic operational matrix, and operational matrix of fractional integral based on the Lerch polynomials have been constructed. The main characteristic of this method is to reduce the stochastic fractional differential equation into a system of algebraic equations by using derived operational matrices and suitable collocation points. Moreover, the convergence and error analysis of the presented method is also discussed in detail. Additionally, the applicability of the proposed technique is also demonstrated by solving some examples. To confirm the accuracy and effectiveness of the suggested technique, a comparison between the results produced by the proposed method and those obtained by other methods has been provided.

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Numerical solution of stochastic Itô-Volterra integral equations based on Bernstein multi-scaling polynomials

Cited by 6 publications

References 19 publications

A Long Short-Term Memory Based Neural Network Approach for Numerical Solutions of Integral Equations

A Long Short-Term Memory Based Neural Network Approach for Numerical Solutions of Integral Equations

A collocation method for the numerical solution of a class of linear stochastic integral equations based on Legendre polynomials

Numerical Treatment for the Solution of Stochastic Fractional Differential Equation Using Lerch Operational Matrix Method

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