One linear analytic approximation for stochastic integrodifferential equations

Numerical solution of nonlinear stochastic Itô‐Volterra integral equations driven by fractional Brownian motion

“…Such phenomena are modeled as stochastic differential equations, 1-4 stochastic integral equations, [5][6][7][8] and stochastic integro-differential equations. [9][10][11] In many cases, these equations cannot be solved analytically, so it is very important to achieved their approximate solution with high accuracy. There are various approach for evaluating the approximate solution of these equations, for example, Petrov-Galerkin method, 12 meshless method, 13,14 wavelet method, 15,16 and operational matrix method.…”

Numerical Solution of Stochastic Ito-Volterra Integral Equations using Haar Wavelets

“…In previous works various numerical methods have been used for approximate the solution of SFEs. Here we only mention Kloeden and Platen [1], Oksendal [2], Maleknejad et al [3,4], Cortes et al [5,6], Murge et al [7], Khodabin et al [8,9], Zhang [10,11], Jankovic [12] and Heydari et al [13].…”

An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics

“…Also, nowadays, there is an increasing demand to investigate the behavior of even more sophisticated dynamical systems in physical, medical, engineering and financial applications [6][7][8][9][10][11][12][13]. These systems often depend on a noise source, like a Gaussian white noise, governed by certain probability laws, so that modeling such phenomena naturally involves the use of various stochastic differential equations (SDEs) [4,[14][15][16][17][18][19][20], or in more complicated cases, stochastic Volterra integral equations and stochastic integro-differential equations [21][22][23][24][25][28][29][30]. In most cases it is difficult to solve such problems explicitly.…”