Tau-collocation Method for Linear Stochastic ˆIto-Volterra Integral Equations

Subject Areas : Applied Mathematics

Somayeh Haghayeghi ¹ (Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran)
Fatemeh Mahmoodi ² (Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran)
Mehdi Omidvari ³ (Department of Mathematics, Abarkouh Branch, Islamic Azad University, Abarkouh, Iran)

Received: 2024-01-05 Accepted : 2024-01-05 Published : 2024-08-04

Keywords: stochastic ˆ ItoVolterra integral equations, Tau-Collocation method, Brownian motion process, Gauss quadrature,

Abstract :

In this work, we propose a numerical Tau-collocation method for obtaining approximate solutions of linear stochastic ˆIto-Volterra integral equations. The method is based on a combination of the successive approximations method, the Gauss quadrature formulas and ˆIto approximation. The applicability of the present method is investigated through illustrative examples.