Numerical solution of stochastic Volterra integral equations by a stochastic operational matrix based on block pulse functions
Reads0
Chats0
TLDR
By using block pulse functions and their stochastic operational matrix of integration, a stochastically Volterra integral equation can be reduced to a linear lower triangular system, which can be directly solved by forward substitution.About:
This article is published in Mathematical and Computer Modelling.The article was published on 2012-02-01 and is currently open access. It has received 95 citations till now. The article focuses on the topics: Volterra integral equation & Stratonovich integral.read more
Citations
More filters
Journal ArticleDOI
A computational method for solving stochastic Itô-Volterra integral equations based on stochastic operational matrix for generalized hat basis functions
TL;DR: A new computational method based on the generalized hat basis functions for solving stochastic Ito–Volterra integral equations is proposed and it is shown that it is O ( 1 n 2 ) .
Journal ArticleDOI
Application of orthonormal Bernstein polynomials to construct a efficient scheme for solving fractional stochastic integro-differential equation
Farshid Mirzaee,Nasrin Samadyar +1 more
TL;DR: In this article, the authors apply operational matrices method based on orthonormal Bernstein polynomials (OBPs) to solve fractional stochastic integro-differential equations.
Journal ArticleDOI
Chebyshev cardinal wavelets and their application in solving nonlinear stochastic differential equations with fractional Brownian motion
TL;DR: A new computational method is proposed to solve a class of nonlinear stochastic differential equations (SDEs) driven by fractional Brownian motion, based on a new class of orthogonal wavelets, namely the Chebyshev cardinal wavelets.
Journal ArticleDOI
A numerical method for solving m-dimensional stochastic Itô-Volterra integral equations by stochastic operational matrix
TL;DR: By using block pulse functions and their stochastic operational matrix of integration, m-dimensional stochastically Ito-Volterra integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution.
Journal ArticleDOI
Numerical solution of stochastic fractional integro-differential equation by the spectral collocation method
TL;DR: The shifted Legendre spectral collocation method is proposed to solve stochastic fractional integro-differential equations (SFIDEs) and it reduces SFIDEs into a system of algebraic equations.
References
More filters
Book
Numerical Solution of Stochastic Differential Equations
Peter E. Kloeden,Eckhard Platen +1 more
TL;DR: In this article, a time-discrete approximation of deterministic Differential Equations is proposed for the stochastic calculus, based on Strong Taylor Expansions and Strong Taylor Approximations.
Reference BookDOI
Stochastic partial differential equations
TL;DR: Preliminaries Linear and Semilinear Wave Equations of the Second Order Asymptotic Behavior of Solutions Introduction Ito's Formula and Lyapunov Functionals Boundedness of Solutions Stability of Null Solution Invariant Measures Small Random Perturbation Problems Large deviation Problems Large deviations Problems as mentioned in this paper.
Book
Matlab, An Introduction With Applications
TL;DR: MATLAB: An Introduction with Applications 4th Edition walks readers through the ins and outs of this powerful software for technical computing, generously illustrated through computer screen shots and step-by-step tutorials.
Book ChapterDOI
Stochastic partial differential equations
TL;DR: In this paper, the general theory developed in Chapter 2 to solve various stochastic partial differential equations (SPDEs) was applied to solve some of the basic SPDEs that appear frequently in applications.
Book
Piecewise Constant Orthogonal Functions and Their Application to Systems and Control
TL;DR: In this article, the authors proposed piecewise constant orthogonal basis functions (PCF) for linear and non-linear linear systems, and the optimal control of linear lag-free and time-lag systems.