Second kind Chebyshev wavelet Galerkin method for stochastic Itô-Volterra integral equations
type: Item
instance of: scholarly article
title: Second kind Chebyshev wavelet Galerkin method for stochastic Itô-Volterra integral equations
zbMATH Open document ID: 1359.65015
author: F. Mohammadi
published in: Mediterranean Journal of Mathematics
publication date: 2016-12-07T00:00:00Z
review text: Using a stochastic operational matrix for the second kind Chebyshev wavelets used as a basis, a Galerkin approximation scheme is devised to obtain numerical approximations for the solution of an Itô stochastic Volterra integral equation of the form \[ X(t)= f(t)+ \int^t_0 \alpha(s, X(s))\,ds + \int^t_0 \sigma(s,X(s))\,dB(s),\quad t\in[0,T), \] where \(B(t)\) is a Brownian motion process. \(L^2\) convergence of the approximate solutions to the exact solution is proved. For three examples numerical results from this method are compared with the exact solution and with results from other numerical methods to illustrate the accuracy and efficiency of this method.
reviewed by: Melvin D. Lax
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 60H20
Mathematics Subject Classification ID: 60H35
Mathematics Subject Classification ID: 45R05
zbMATH DE Number: 6661791
zbMATH Keywords: second kind Chebyshev wavelets
zbMATH Keywords: Itô integral
zbMATH Keywords: stochastic operational matrix
zbMATH Keywords: stochastic Itô-Volterra integral equations
zbMATH Keywords: Brownian motion
zbMATH Keywords: numerical results
MaRDI profile type: Publication
full work available at URL: s00009-015-0642-z
OpenAlex ID: W2183556908
cites work: Q4004325
cites work: Stochastic differential equations. An introduction with applications.
cites work: An algorithmic introduction to numerical simulation of stochastic differential equations
cites work: Numerical solution of stochastic Volterra integral equations by a stochastic operational matrix based on block pulse functions
cites work: Numerical approach for solving stochastic Volterra-Fredholm integral equations by stochastic operational matrix
cites work: Q6162228
cites work: A computational method for solving stochastic Itô-Volterra integral equations based on stochastic operational matrix for generalized hat basis functions
cites work: An efficient computational method for solving nonlinear stochastic Itô integral equations: application for stochastic problems in physics
cites work: A wavelet-based computational method for solving stochastic Itô-Volterra integral equations
cites work: Q2941222
cites work: Successive approximations for solutions of second order stochastic integrodifferential equations of Ito type
cites work: Numerical solution of random differential equations: a mean square approach
cites work: One linear analytic approximation for stochastic integrodifferential equations
cites work: Wavelets and Dilation Equations: A Brief Introduction
cites work: Q3391609
cites work: Fast wavelet transforms and numerical algorithms I
cites work: The Legendre wavelets operational matrix of integration
cites work: Numerical solution of differential equations using Haar wavelets
cites work: Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration
cites work: Solving a nonlinear fractional differential equation using Chebyshev wavelets
cites work: Chebyshev wavelet method for numerical solution of Fredholm integral equations of the first kind
cites work: Legendre wavelet method for numerical solutions of partial differential equations
cites work: Legendre wavelet Galerkin method for solving ordinary differential equations with non-analytic solution
cites work: Q2974582
cites work: An extended Legendre wavelet method for solving differential equations with non analytic solutions
cites work: On the Congruences in Right Loops
cites work: The second kind Chebyshev wavelet method for solving fractional differential equations
cites work: Solving fractional nonlinear Fredholm integro-differential equations by the second kind Chebyshev wavelet
cites work: Q4791752
DOI: 10.1007/S00009-015-0642-Z
description: scientific article; zbMATH DE number 6661791