Numerical Solution of Multidimensional Stochastic Itô-Volterra Integral Equation Based on the Least Squares Method and Block Pulse Function

In this paper, a method based on the least squares method and block pulse function is proposed to solve the multidimensional stochastic Itô-Volterra integral equation. The Itô-Volterra integral equation is transformed into a linear algebraic equation. Furthermore, the error analysis is given by the isometry property and Doob’s inequality. Numerical examples verify the effectiveness and precision of this method.

A stochastic operational matrix method for numerical solutions of multi-dimensional stochastic Itô–Volterra integral equations

In this article, hybrid Legendre block-pulse functions are implemented in determining the approximate solutions for multi-dimensional stochastic Itô–Volterra integral equations. The block-pulse function and the proposed scheme are used for deriving a methodology to obtain the stochastic operational matrix. Error and convergence analysis of the scheme is discussed. A brief discussion including numerical examples has been provided to justify the efficiency of the mentioned method.

Computational Block-Pulse Functions Method for Solving Volterra Integral Equations with Delay

The aim of this work is to present method of the Block-pulse function approach to numerical solution of Volterra integral equations with delay. This method is used to obtain numerical solution. Moreover, programs for his method is written in MATLAB language. An error analysis is worked out and applications demonstrated through illustrative examples

Study of Nonlinear Observer for Dynamic Friction Compensation of High-Accuracy Servo-System

In this paper, a nonlinear observer is designed for a servo system with non-linear dynamic friction. With this kind of observer, the dynamic friction can be estimated and then be compensated using the input and output data on-line. A recursive formula of the nonlinear observer is derived by using the block pulse function which can be easily implemented on-line with microcomputers. The designed non-linear observer is applied to high accuracy servo system running at very low speed and prove to be effective and satisfactory.