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 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 Fixed Points and Continuity for a Pair of Contractive Maps with Application to Nonlinear Volterra Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Santosh Kumar
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Volterra Integral Equations ◽  
Discontinuous Mappings ◽  
Contractive Maps ◽  
Uniqueness Of A Solution ◽  
Type Contraction

In this paper, we have established and proved fixed point theorems for the Boyd-Wong-type contraction in metric spaces. In particular, we have generalized the existing results for a pair of mappings that possess a fixed point but not continuous at the fixed point. We can apply this result for both continuous and discontinuous mappings. We have concluded our results by providing an illustrative example for each case and an application to the existence and uniqueness of a solution of nonlinear Volterra 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 Fixed-Point Theorem for Nonlinear F -Contraction via w -Distance

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Abdelkarim Kari ◽  
Mohamed Rossafi ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Fredholm Integral Equations ◽  
Nonlinear Fredholm Integral Equations ◽  
Uniqueness Of A Solution

The aim of this paper is to introduce a notion of ϕ , F -contraction defined on a metric space with w -distance. Moreover, fixed-point theorems are given in this framework. As an application, we prove the existence and uniqueness of a solution for the nonlinear Fredholm integral equations. Some illustrative examples are provided to advocate the usability of our results.

scholarly journals C*-Algebra Valued Partial b-Metric Spaces and Fixed Point Results with an Application

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1381
Author(s):  
Nabil Mlaiki ◽  
Mohammad Asim ◽  
Mohammad Imdad
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fredholm Integral Equations ◽  
Partial Metric ◽  
C Algebra ◽  
Partial Metric Spaces ◽  
Uniqueness Of A Solution

In this paper, we enlarge the class of C*-algebra valued partial metric spaces as well as the class of C*-algebra valued b-metric spaces by introducing the class of C*-algebra valued partial b-metric spaces and utilize the same to prove our fixed point results. We furnish an example to highlight the utility of our main result. Finally, we apply our result in order to examine the existence and uniqueness of a solution for the system of Fredholm 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 Fixed Point Results in Partial Symmetric Spaces with an Application

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 13 ◽  
Author(s):  
Mohammad Asim ◽  
A. Khan ◽  
Mohammad Imdad
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Symmetric Spaces ◽  
Fixed Point Theorems ◽  
Hausdorff Metric ◽  
Contraction Principle ◽  
Fredholm Integral Equations ◽  
Uniqueness Of A Solution

In this paper, we first introduce the class of partial symmetric spaces and then prove some fixed point theorems in such spaces. We use one of the our main results to examine the existence and uniqueness of a solution for a system of Fredholm integral equations. Furthermore, we introduce an analogue of the Hausdorff metric in the context of partial symmetric spaces and utilize the same to prove an analogue of the Nadler contraction principle in such spaces. Our results extend and improve many results in the existing literature. We also give some examples exhibiting the utility of our newly established results.

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