Nonlinear wave interaction of three Stokes’ waves in deep water: Banach fixed point method

2006 ◽  
Vol 20 (11) ◽  
pp. 1950-1960
Author(s):  
Taek S. Jang ◽  
S. H. Kwon ◽  
Beom J. Kim
Keyword(s):  
Fixed Point ◽  
Nonlinear Wave ◽  
Deep Water ◽  
Wave Interaction ◽  
Fixed Point Method ◽  
Point Method ◽  
Nonlinear Wave Interaction ◽  
Stokes Waves

scholarly journals Analytical Solutions for the Elastic Circular Rod Nonlinear Wave, Boussinesq, and Dispersive Long Wave Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Shi Jing ◽  
Yan Xin-li
Keyword(s):  
Fixed Point ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Expansion Method ◽  
Mapping Method ◽  
Fixed Point Method ◽  
Point Method ◽  
Nonlinear Wave Equations ◽  
Jacobi Elliptic Function ◽  
Long Wave

The solving processes of the homogeneous balance method, Jacobi elliptic function expansion method, fixed point method, and modified mapping method are introduced in this paper. By using four different methods, the exact solutions of nonlinear wave equation of a finite deformation elastic circular rod, Boussinesq equations and dispersive long wave equations are studied. In the discussion, the more physical specifications of these nonlinear equations, have been identified and the results indicated that these methods (especially the fixed point method) can be used to solve other similar nonlinear wave equations.

A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4933-4944
Author(s):  
Dongseung Kang ◽  
Heejeong Koh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Single Case ◽  
Fixed Point Method ◽  
Point Method ◽  
Fixed Point Approach ◽  
The Stability ◽  
The Given ◽  
Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

scholarly journals Ulam-Hyers Stability and Ulam-Hyers-Rassias Stability for Fuzzy Integrodifferential Equation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Nguyen Ngoc Phung ◽  
Bao Quoc Ta ◽  
Ho Vu
Keyword(s):  
Fixed Point ◽  
Successive Approximation ◽  
Integrodifferential Equation ◽  
Approximation Method ◽  
Fixed Point Method ◽  
Integrodifferential Equations ◽  
Point Method ◽  
Successive Approximation Method ◽  
Rassias Stability

In this paper, we establish the Ulam-Hyers stability and Ulam-Hyers-Rassias stability for fuzzy integrodifferential equations by using the fixed point method and the successive approximation method.

scholarly journals Homomorphisms and derivations in C∗-ternary algebras via fixed point method

2012 ◽  
Vol 2012 (1) ◽  
pp. 137 ◽  
Author(s):  
HM Kenari ◽  
Reza Saadati ◽  
Choonkil Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Ternary Algebras

scholarly journals Sets of Fractional Operators and Numerical Estimation of the Order of Convergence of a Family of Fractional Fixed-Point Methods

2021 ◽  
Vol 5 (4) ◽  
pp. 240
Author(s):  
A. Torres-Hernandez ◽  
F. Brambila-Paz
Keyword(s):  
Fixed Point ◽  
Fractional Calculus ◽  
Order Of Convergence ◽  
Convergent Sequence ◽  
Scalar Function ◽  
Fixed Point Method ◽  
Point Method ◽  
Fractional Operators ◽  
Fixed Point Methods ◽  
Vector Valued Function

Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a simple and compact method to work the fractional calculus through the classification of fractional operators using sets. This new method of working with fractional operators, which may be called fractional calculus of sets, allows generalizing objects of conventional calculus, such as tensor operators, the Taylor series of a vector-valued function, and the fixed-point method, in several variables, which allows generating the method known as the fractional fixed-point method. Furthermore, it is also shown that each fractional fixed-point method that generates a convergent sequence has the ability to generate an uncountable family of fractional fixed-point methods that generate convergent sequences. So, it is presented a method to estimate numerically in a region Ω the mean order of convergence of any fractional fixed-point method, and it is shown how to construct a hybrid fractional iterative method to determine the critical points of a scalar function. Finally, considering that the proposed method to classify fractional operators through sets allows generalizing the existing results of the fractional calculus, some examples are shown of how to define families of fractional operators that satisfy some property to ensure the validity of the results to be generalized.

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