scholarly journals Solving nonlinear integral equations for laser pulse retrieval with Newton's method

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Michael Jasiulek
Keyword(s):  
Laser Pulse ◽  
Integral Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Nonlinear Integral Equations

scholarly journals How to Obtain Global Convergence Domains via Newton’s Method for Nonlinear Integral Equations

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 553 ◽  
Author(s):  
José Antonio Ezquerro ◽  
Miguel Ángel Hernández-Verón
Keyword(s):  
Global Convergence ◽  
Integral Equations ◽  
Newton’S Method ◽  
Existence And Uniqueness ◽  
Newton's Method ◽  
Uniqueness Of Solution ◽  
Nonlinear Integral Equations ◽  
Theoretical Significance

We use the theoretical significance of Newton’s method to draw conclusions about the existence and uniqueness of solution of a particular type of nonlinear integral equations of Fredholm. In addition, we obtain a domain of global convergence for Newton’s method.

scholarly journals An application of Newton's method to differential and integral equations

2001 ◽  
Vol 42 (3) ◽  
pp. 372-386 ◽  
Author(s):  
J. M. Gutiérrez ◽  
M. A. Hernández
Keyword(s):  
Integral Equations ◽  
Error Estimates ◽  
Newton’S Method ◽  
Existence And Uniqueness ◽  
Newton's Method ◽  
Uniqueness Of A Solution ◽  
Differential And Integral Equations

AbstractNewton's method is applied to an operator that satisfies stronger conditions than those of Kantorovich. Convergence and error estimates are compared in the two situations. As an application, we obtain information on the existence and uniqueness of a solution for differential and integral equations.

scholarly journals A Picard-Type Iterative Scheme for Fredholm Integral Equations of the Second Kind

Mathematics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 83
Author(s):  
José M. Gutiérrez ◽  
Miguel Á. Hernández-Verón
Keyword(s):  
Iterative Method ◽  
Banach Spaces ◽  
Integral Equations ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Quadratic Convergence ◽  
Iterative Scheme ◽  
Fredholm Integral Equations

In this work, we present an application of Newton’s method for solving nonlinear equations in Banach spaces to a particular problem: the approximation of the inverse operators that appear in the solution of Fredholm integral equations. Therefore, we construct an iterative method with quadratic convergence that does not use either derivatives or inverse operators. Consequently, this new procedure is especially useful for solving non-homogeneous Fredholm integral equations of the first kind. We combine this method with a technique to find the solution of Fredholm integral equations with separable kernels to obtain a procedure that allows us to approach the solution when the kernel is non-separable.

scholarly journals Numerical solution of system of two Nonlinear Volterra Integral equations

2014 ◽  
Vol 12 (10) ◽  
pp. 3967-3975
Author(s):  
Dalal Adnan Maturi
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Trapezoidal Rule ◽  
Volterra Integral Equations ◽  
Implicit Trapezoidal Rule

In this paper, using the implicit trapezoidal rule in conjunction with Newton's method to solve nonlinear system.We have used a Maple 17 program to solve the System of two nonlinear Volterra integral equations. Finally, several illustrative examples are presented to show the effectiveness and accuracy of this method.

Optimal Power Flow Using Newton’s Method

2012 ◽  
Vol 3 (2) ◽  
pp. 167-169
Author(s):  
F.M.PATEL F.M.PATEL ◽  
◽  
N. B. PANCHAL N. B. PANCHAL
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Optimal Power

An Efficient Sixth-Order Convergent Newton-Type Iterative Method for Nonlinear Equations

2012 ◽  
Vol 220-223 ◽  
pp. 2585-2588
Author(s):  
Zhong Yong Hu ◽  
Fang Liang ◽  
Lian Zhong Li ◽  
Rui Chen
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Efficiency Index ◽  
Sixth Order ◽  
Type Method ◽  
Second Derivatives ◽  
Better Than

In this paper, we present a modified sixth order convergent Newton-type method for solving nonlinear equations. It is free from second derivatives, and requires three evaluations of the functions and two evaluations of derivatives per iteration. Hence the efficiency index of the presented method is 1.43097 which is better than that of classical Newton’s method 1.41421. Several results are given to illustrate the advantage and efficiency the algorithm.

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