A comparison between Newton's method and A.D.M for solving special Fredholm integral equations

2007 ◽  
Vol 2 ◽  
pp. 215-222
Author(s):  
J. Biazar ◽  
A. Ranjbar
Keyword(s):  
Integral Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Fredholm 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 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 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.

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 Cooperating Newton’s Method with Series Solution Method for Solving System of Linear Mixed Volterra-Fredholm Integral Equation of the Second Kind

2019 ◽  
Vol 3 (1) ◽  
pp. 27-33
Author(s):  
Talaat I. Hasan
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Series Solution ◽  
Solution Method ◽  
Numerical Solutions ◽  
Least Square ◽  
Fredholm Integral Equations ◽  
Numerical Examples ◽  
Matlab Program ◽  
A New Technique

In this paper, for the 1st time, we use Newton’s method with series solution method (SSM) for solving system of linear mixed Volterra-Fredholm integral equations of the second kind (SLMVFIE-2). In this work, we use a new technique for studying the numerical solutions for SLMVFIE-2 which is Newton’s method with SSM, first solving this system using SSM and after that cooperation Newton’s method with SSM, suggesting an algorithm for the technique. The new results are achieved and some new theorems have proved for convergence of the method, several numerical examples are tested for illustrating the usefulness of the technique; the numerical results are obtained and compared with the exact solution, computing the least square error, and running times which are criterion of discussion. For programming the technique, we use general Matlab program.

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
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