Spectral Solutions with Error Analysis of Volterra–Fredholm Integral Equation via Generalized Lucas Collocation Method

2021 ◽  
Vol 7 (5) ◽  
Author(s):  
A. S. Mohamed
Keyword(s):  
Integral Equation ◽  
Error Analysis ◽  
Collocation Method ◽  
Fredholm Integral Equation

Numerical Solution of Nonlinear Volterra-Fredholm Integral Equations Using Haar Wavelet Collocation Method

2017 ◽  
Vol 18 ◽  
pp. 50-59 ◽  
Author(s):  
S.C. Shiralashetti ◽  
R.A. Mundewadi
Keyword(s):  
Integral Equation ◽  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Collocation Method ◽  
Haar Wavelet ◽  
Fredholm Integral Equations ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Wavelet Collocation Method

In this paper, we present a numerical solution of nonlinear Volterra-Fredholm integral equations using Haar wavelet collocation method. Properties of Haar wavelet and its operational matrices are utilized to convert the integral equation into a system of algebraic equations, solving these equations using MATLAB to compute the Haar coefficients. The numerical results are compared with exact and existing method through error analysis, which shows the efficiency of the technique.

scholarly journals Chebyshev collocation treatment of Volterra–Fredholm integral equation with error analysis

2019 ◽  
Vol 9 (2) ◽  
pp. 471-480 ◽  
Author(s):  
Y. H. Youssri ◽  
R. M. Hafez
Keyword(s):  
Integral Equation ◽  
Error Analysis ◽  
Numerical Solution ◽  
Fredholm Integral Equation ◽  
Chebyshev Polynomials ◽  
Matrix Equation ◽  
Chebyshev Collocation ◽  
Chebyshev Nodes ◽  
Potential Applicability ◽  
The Given

Abstract This work reports a collocation algorithm for the numerical solution of a Volterra–Fredholm integral equation (V-FIE), using shifted Chebyshev collocation (SCC) method. Some properties of the shifted Chebyshev polynomials are presented. These properties together with the shifted Gauss–Chebyshev nodes were then used to reduce the Volterra–Fredholm integral equation to the solution of a matrix equation. Nextly, the error analysis of the proposed method is presented. We compared the results of this algorithm with others and showed the accuracy and potential applicability of the given method.

scholarly journals Numerical Solution of Volterra-Fredholm Integral Equations with Hosoya Polynomials

2021 ◽  
Author(s):  
Ercan Çelik ◽  
Merve Geçmen
Keyword(s):  
Integral Equation ◽  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Programming Language ◽  
Fredholm Integral Equation ◽  
Fredholm Integral Equations ◽  
Matlab Programming

In this study, Volterra-Fredholm integral equation is solved by Hosoya Polynomials. The solutions obtained with these methods were compared on the figure and table. And error analysis was done. Matlab programming language has been used to obtain conclusitions, tables and error analysis within a certain algorithm.

Sign in / Sign up

Export Citation Format

Share Document