A new technique for the numerical solution of Fredholm integral equations

Computing ◽  
1968 ◽  
Vol 3 (2) ◽  
pp. 131-138 ◽  
Author(s):  
R. Bellman
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
New Technique ◽  
Fredholm Integral Equations ◽  
A New Technique

scholarly journals Solving Linear Volterra – Fredholm Integral Equation of the Second Type Using Linear Programming Method

2020 ◽  
Vol 17 (1(Suppl.)) ◽  
pp. 0342
Author(s):  
Muna Mansoor Mustafaf
Keyword(s):  
Linear Programming ◽  
Integral Equations ◽  
New Technique ◽  
Fredholm Integral Equations ◽  
Quadrature Methods ◽  
Special Cases ◽  
A New Technique ◽  
Linear Integral ◽  
Romberg Integration ◽  
Linear Integral Equations

In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods is produced. Finally, for more explanation, an algorithm is proposed and applied for testing examples to illustrate the effectiveness of the new technique.

scholarly journals A Comparative Study on Haar Wavelet and Hosaya Polynomial for the numerical solution of Fredholm integral equations

2018 ◽  
Vol 3 (2) ◽  
pp. 447-458 ◽  
Author(s):  
S.C. Shiralashetti ◽  
H. S. Ramane ◽  
R.A. Mundewadi ◽  
R.B. Jummannaver
Keyword(s):  
Error Analysis ◽  
Comparative Study ◽  
Numerical Solution ◽  
Integral Equations ◽  
Haar Wavelet ◽  
Fredholm Integral Equations ◽  
Polynomial Method ◽  
Wavelet Method ◽  
Haar Wavelet Method ◽  
Hosoya Polynomial

AbstractIn this paper, a comparative study on Haar wavelet method (HWM) and Hosoya Polynomial method(HPM) for the numerical solution of Fredholm integral equations. Illustrative examples are tested through the error analysis for efficiency. Numerical results are shown in the tables and figures.

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