An efficient newton's method for the numerical solution of fluid integral equations

1985 ◽  
Vol 61 (2) ◽  
pp. 280-285 ◽  
Author(s):  
Gilles Zerah
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Newton’S Method ◽  
Newton's Method

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.

The Application of Newton’s Method to the Problem of Elastic Stability

1972 ◽  
Vol 39 (4) ◽  
pp. 1060-1065 ◽  
Author(s):  
E. Riks
Keyword(s):  
Numerical Solution ◽  
Newton’S Method ◽  
Iteration Method ◽  
Newton's Method ◽  
Elastic Stability ◽  
Auxiliary Equation

The numerical solution of problems of elastic stability through the use of the iteration method of Newton is examined. It is found that if the equations of equilibrium are completed by a simple auxiliary equation, problems governed by a snapping condition can, in principle, always be calculated as long as the problem at hand is properly formulated. The effectiveness of the proposed procedure is demonstrated by means of an elementary example.

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.

Algorithms for Solving the Catch Equation Forward and Backward in Time

1982 ◽  
Vol 39 (1) ◽  
pp. 197-202 ◽  
Author(s):  
S. E. Sims
Keyword(s):  
Mortality Rate ◽  
Numerical Solution ◽  
Exponential Function ◽  
Newton’S Method ◽  
Newton's Method ◽  
Padé Approximation ◽  
Approximate Solutions ◽  
Fishing Mortality ◽  
Convergence Criteria ◽  
Pade Approximation

Approximate solutions to the catch equation for the fishing mortality rate both forward and backward in time are obtained with an application of the diagonal Padé approximation of degree four to the exponential function. In either case the resulting approximation as well as Pope's estimate are shown to serve quite well as starting values for Newton's Method which is used to obtain a numerical solution of the catch equation. Convergence criteria for Newton's Method are discussed in each setting.Key words: catch equation, Newton's method, Padé approximation, Pope's estimate

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