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.

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