A numerical method for solving stochastic Ito-Volterra integral equation with multi stochastic terms by modified hat functions and improved hat functions

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Momenzadeh Neda; Vahidi Alireza; Babolian Esmail

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Journal Paper

Paper Information

Journal: Mathematical Researches Year:2023 | Volume:9 | Issue:1 Page(s): 222-245

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Information Journal Paper

Title

A numerical method for solving stochastic Ito-Volterra integral equation with multi stochastic terms by modified hat functions and improved hat functions

Author(s)

Momenzadeh Neda | Vahidi Alireza | Babolian Esmail | Issue Writer Certificate

Keywords

Stochastic integral equations

Brownian motionModified hat functions

Operational matrix

Abstract

In this paper, modified hat functions and improved hat functions are proposed to solve stochastic Ito ̂-Volterra integral equations with multi stochastic terms. A linear system of equations are achieved by replacing the vector and matrix coefficients and operational matrices in the equation which is easy to solve with mathematical softwares. Also, under some conditions the error of these methods are o(h^3) and o(h^4 ) . The accuracy and reliability of these two methods are studied by solving and comparing the answers with block pulse functions and hat functions.

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