A numerical method for solving \(m\)-dimensional stochastic itô-Volterra integral equations by stochastic operational matrix

DOI10.1016/j.camwa.2011.10.079zbMath1238.65007OpenAlexW2048693776MaRDI QIDQ418302

Madjid Rostami, Morteza Khodabin, Khosrow Maleknejad

Publication date: 28 May 2012

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2011.10.079

zbMATH Keywords

Itô integralVolterra integral equationsstochastic operational matrixblock pulse functionsBrownian motion processstochastic Itô

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Numerical solutions to stochastic differential and integral equations (65C30) Stochastic integral equations (60H20) Random integral equations (45R05)

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Cites Work

• Unnamed Item
• Unnamed Item
• Interpolation solution in generalized stochastic exponential population growth model
• One linear analytic approximation for stochastic integrodifferential equations
• Numerical solution of stochastic differential equations by second order Runge-Kutta methods
• Modification of block pulse functions and their application to solve numerically Volterra integral equation of the first kind
• Stochastic Volterra equations in Banach spaces and stochastic partial differential equation
• Euler schemes and large deviations for stochastic Volterra equations with singular kernels
• Piecewise constant orthogonal functions and their application to systems and control
• Numerical solution of linear Fredholm integral equation by using hybrid Taylor and Block-Pulse functions.
• Approximation schemes for Itô-Volterra stochastic equations
• Numerical solution of stochastic Volterra integral equations by a stochastic operational matrix based on block pulse functions
• Numerical solution of nonlinear Volterra integral equations of the second kind by using Chebyshev polynomials
• Numerical solution of random differential equations: a mean square approach
• An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
• Numerical solution of an integral equations system of the first kind by using an operational matrix with block pulse functions
• Recursive computational algorithms for a set of block pulse operational matrices
• Stochastic differential equations. An introduction with applications.

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