On the Approximation Solutions of linear and nonlinear Volterra Integral Equation of First and Second kinds by Using B-spline Tight Framelets Generated by Unitary Extension Principle and Oblique Extension Principle

2020 ◽  
Vol 15 (2) ◽  
pp. 165-189
Author(s):  
Yousef Al-Jarrah
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation ◽  
Extension Principle ◽  
B Spline ◽  
Nonlinear Volterra Integral Equation ◽  
Unitary Extension ◽  
Linear And Nonlinear

scholarly journals Solving three-dimensional Volterra integral equation by the reduced differential transform method

2016 ◽  
Vol 5 (2) ◽  
pp. 103 ◽  
Author(s):  
Abdelhalim Ziqan ◽  
Sawsan Armiti ◽  
Iyad Suwan
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation ◽  
Three Dimensional ◽  
Differential Transform Method ◽  
Transform Method ◽  
Nonlinear Volterra Integral Equation ◽  
Differential Transform ◽  
Linear And Nonlinear ◽  
Reduced Differential Transform Method ◽  
Number Of Iterations

<p>In this article, the results of two-dimensional reduced differential transform method is extended to three-dimensional case for solving three dimensional Volterra integral equation. Using the described method, the exact solution can be obtained after a few number of iterations. Moreover, examples on both linear and nonlinear Volterra integral equation are carried out to illustrate the efficiency and the accuracy of the presented method.</p>

scholarly journals Solving volterra integral equation via nonlinear programming

2016 ◽  
Vol 5 (4) ◽  
pp. 192
Author(s):  
Jamal Othman
Keyword(s):  
Integral Equation ◽  
Nonlinear Programming ◽  
Volterra Integral Equation ◽  
Least Square ◽  
Nonlinear Programming Problem ◽  
Programming Technique ◽  
New Approach ◽  
Nonlinear Volterra Integral Equation ◽  
Limited Memory ◽  
Quasi Newton

In this paper we propose an approach to find approximate solution to the nonlinear Volterra integral equation of the second type through a nonlinear programming technique by firstly converting the integral equation into a least square cost function as an objective function for an unconstrained nonlinear programming problem which solved by a nonlinear programming technique (The preconditioned limited- memory quasi-Newton conjugates, gradient method) and as far as we read this is a new approach in the ways of solving the nonlinear Volterra integral equation. We use Maple 11 software as a tool for performing the suggested steps in solving the examples.

scholarly journals Nonlinear Volterra Integral Equation of the Second Kind and Biorthogonal Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
M. I. Berenguer ◽  
D. Gámez ◽  
A. I. Garralda-Guillem ◽  
M. C. Serrano Pérez
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Volterra Integral Equation ◽  
Biorthogonal System ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Volterra Integral Equation ◽  
Numerical Resolution

We obtain an approximation of the solution of the nonlinear Volterra integral equation of the second kind, by means of a new method for its numerical resolution. The main tools used to establish it are the properties of a biorthogonal system in a Banach space and the Banach fixed point theorem.

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