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

2019 ◽  
Vol 27 (1) ◽  
pp. 32-42
Author(s):  
Hameed Kadhim Dawood
Keyword(s):  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Present Method ◽  
Volterra Integral Equations ◽  
Function Approach ◽  
Block Pulse Functions ◽  
Block Pulse Function ◽  
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

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

2020 ◽  
Vol 28 (3) ◽  
pp. 209-216
Author(s):  
S. Singh ◽  
S. Saha Ray
Keyword(s):  
Integral Equations ◽  
Numerical Solutions ◽  
Operational Matrix ◽  
Approximate Solutions ◽  
Volterra Integral Equations ◽  
Numerical Examples ◽  
Operational Matrix Method ◽  
Block Pulse Functions ◽  
Stochastic Operational Matrix ◽  
Block Pulse Function

AbstractIn 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.

scholarly journals Modified Block Pulse Functions for Numerical Solution of Stochastic Volterra Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
K. Maleknejad ◽  
M. Khodabin ◽  
F. Hosseini Shekarabi
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Rate Of Convergence ◽  
Integral Equations ◽  
Volterra Integral Equation ◽  
Volterra Integral Equations ◽  
Numerical Example ◽  
Block Pulse Functions ◽  
A New Technique ◽  
Modified Block

We present a new technique for solving numerically stochastic Volterra integral equation based on modified block pulse functions. It declares that the rate of convergence of the presented method is faster than the method based on block pulse functions. Efficiency of this method and good degree of accuracy are confirmed by a numerical example.

Solving systems of fractional two-dimensional nonlinear partial Volterra integral equations by using Haar wavelets

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Amir Ahmad Khajehnasiri ◽  
R. Ezzati ◽  
M. Afshar Kermani
Keyword(s):  
Nonlinear System ◽  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Fractional Integration ◽  
Volterra Integral Equations ◽  
Haar Wavelets ◽  
Operational Matrices ◽  
Two Dimensional ◽  
Numerical Examples

Abstract The main aim of this paper is to use the operational matrices of fractional integration of Haar wavelets to find the numerical solution for a nonlinear system of two-dimensional fractional partial Volterra integral equations. To do this, first we present the operational matrices of fractional integration of Haar wavelets. Then we apply these matrices to solve systems of two-dimensional fractional partial Volterra integral equations (2DFPVIE). Also, we present the error analysis and convergence as well. At the end, some numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method.

scholarly journals NUMERICAL SOLUTION OF MIXED LINEAR VOLTERRA-FREDHOLM INTEGRAL EQUATIONS BY MODIFIED BLOCK PULSE FUNCTIONS

2021 ◽  
Vol 5 (1) ◽  
pp. 1
Author(s):  
Ayyubi Ahmad
Keyword(s):  
Linear System ◽  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Operational Matrix ◽  
Fredholm Integral Equations ◽  
Algebraic Equations ◽  
Block Pulse Functions ◽  
Operational Matrix Of Integration ◽  
Modified Block

A numerical method based on modified block pulse functions is proposed for solving the mixed linear Volterra-Fredholm integral equations. We obtain an integration operational matrix of modified block pulse functions on interval [0,T). A modified block pulse functions and their operational matrix of integration, the mixed linear Volterra-Fredholm integral equations can be reduced to a linear system of algebraic equations. The rate of convergence is O(h) and error analysis of the proposed method are discussed. Some examples are provided to show that the proposed method have a good degree of accuracy.

scholarly journals Numerical Solution of Two-Dimensional Nonlinear Stochastic Itô-Volterra Integral Equations by Applying Block Pulse Functions

2019 ◽  
Vol 09 (02) ◽  
pp. 53-66 ◽  
Author(s):  
Guo Jiang ◽  
Xiaoyan Sang ◽  
Jieheng Wu ◽  
Biwen Li
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Volterra Integral Equations ◽  
Two Dimensional ◽  
Block Pulse Functions

scholarly journals Numerical solution of nonlinear stochastic Itô–Volterra integral equations based on Haar wavelets

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Jieheng Wu ◽  
Guo Jiang ◽  
Xiaoyan Sang
Keyword(s):  
Approximate Solution ◽  
Error Analysis ◽  
Numerical Solution ◽  
Numerical Method ◽  
Integral Equations ◽  
Volterra Integral Equations ◽  
Haar Wavelets ◽  
Stochastic Integration ◽  
Numerical Examples

AbstractIn this paper, an efficient numerical method is presented for solving nonlinear stochastic Itô–Volterra integral equations based on Haar wavelets. By the properties of Haar wavelets and stochastic integration operational matrixes, the approximate solution of nonlinear stochastic Itô–Volterra integral equations can be found. At the same time, the error analysis is established. Finally, two numerical examples are offered to testify the validity and precision of the presented method.

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

2016 ◽  
Vol 9 (3) ◽  
pp. 416-431 ◽  
Author(s):  
Fakhrodin Mohammadi
Keyword(s):  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
General Procedure ◽  
Operational Matrix ◽  
Volterra Integral Equations ◽  
Computational Method ◽  
Haar Wavelets ◽  
Stochastic Operational Matrix

AbstractThis paper presents a computational method for solving stochastic Ito-Volterra integral equations. First, Haar wavelets and their properties are employed to derive a general procedure for forming the stochastic operational matrix of Haar wavelets. Then, application of this stochastic operational matrix for solving stochastic Ito-Volterra integral equations is explained. The convergence and error analysis of the proposed method are investigated. Finally, the efficiency of the presented method is confirmed by some examples.

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