scholarly journals Shifted Jacobi Collocation Method Based on Operational Matrix for Solving the Systems of Fredholm and Volterra Integral Equations

2015 ◽  
Vol 20 (2) ◽  
pp. 76-93
Author(s):  
A. Borhanifar ◽  
K. Sadri
Keyword(s):  
Integral Equations ◽  
Collocation Method ◽  
Operational Matrix ◽  
Volterra Integral Equations ◽  
Jacobi Collocation Method

scholarly journals A Jacobi-Collocation Method for Second Kind Volterra Integral Equations with a Smooth Kernel

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hongfeng Guo ◽  
Haotao Cai ◽  
Xin Zhang
Keyword(s):  
Integral Operator ◽  
Integral Equations ◽  
Collocation Method ◽  
Volterra Integral Equations ◽  
Numerical Example ◽  
Fully Discrete ◽  
Smooth Kernel ◽  
Jacobi Collocation Method

The purpose of this paper is to provide a Jacobi-collocation method for solving second kind Volterra integral equations with a smooth kernel. This method leads to a fully discrete integral operator. First, it is shown that the fully discrete integral operator is stable in bothL∞and weightedL2norms. Then, the proposed approach is proved to arrive at an optimal (the most possible) convergent order in both norms. One numerical example demonstrates the efficiency and accuracy of the proposed method.

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.

Collocation method for Fredholm and Volterra integral equations

Kybernetes ◽  
2013 ◽  
Vol 42 (3) ◽  
pp. 400-412 ◽  
Author(s):  
Jalil Rashidinia ◽  
Zahra Mahmoodi
Keyword(s):  
Integral Equations ◽  
Collocation Method ◽  
Volterra Integral Equations

Stochastic operational matrix of Chebyshev wavelets for solving multi-dimensional stochastic Itô–Volterra integral equations

2019 ◽  
Vol 17 (03) ◽  
pp. 1950007 ◽  
Author(s):  
S. Singh ◽  
S. Saha Ray
Keyword(s):  
Integral Equations ◽  
Numerical Solutions ◽  
General Procedure ◽  
Operational Matrix ◽  
Volterra Integral Equations ◽  
Algebraic Equations ◽  
Chebyshev Wavelets ◽  
System Of Integral Equations ◽  
Block Pulse Functions ◽  
Stochastic Operational Matrix

In this paper, the numerical solutions of multi-dimensional stochastic Itô–Volterra integral equations have been obtained by second kind Chebyshev wavelets. The second kind Chebyshev wavelets are orthonormal and have compact support on [Formula: see text]. The block pulse functions and their relations to second kind Chebyshev wavelets are employed to derive a general procedure for forming stochastic operational matrix of second kind Chebyshev wavelets. The system of integral equations has been reduced to a system of nonlinear algebraic equations and solved for obtaining the numerical solutions. Convergence and error analysis of the proposed method are also discussed. Furthermore, some examples have been discussed to establish the accuracy and efficiency of the proposed scheme.

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