Construction and Investigation of the Third-Order Approximation to the Solution of the Heat-Conduction Equation for Thin Shallow Shells by Using Legendre Polynomials in the Case of Stationary Heat Exchange

2018 ◽  
Vol 231 (5) ◽  
pp. 608-618
Author(s):  
K. M. Dovbnya ◽  
O. D. Dundar
Keyword(s):  
Heat Conduction ◽  
Heat Exchange ◽  
Legendre Polynomials ◽  
Heat Conduction Equation ◽  
Order Approximation ◽  
Third Order ◽  
Shallow Shells ◽  
Stationary Heat ◽  
The Third ◽  
Third Order Approximation

Effect of the third-order contribution on ion-acoustic solitary waves

1979 ◽  
Vol 57 (12) ◽  
pp. 2136-2142 ◽  
Author(s):  
C. S. Lai
Keyword(s):  
Solitary Waves ◽  
Order Approximation ◽  
Reductive Perturbation Method ◽  
Renormalization Scheme ◽  
Third Order ◽  
The Third ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic ◽  
Third Order Approximation ◽  
Secular Terms

The effect of the third-order corrections on ion-acoustic solitary waves is studied on the basis of the reductive perturbation method. The secular terms in the third-order approximation are eliminated by employing the renormalization scheme of Kodama and Taniuti in an unambiguous manner. It is found that the contribution of the third-order corrections to the soliton velocities and widths is rather minimal.

scholarly journals Approximation by the Third-Order Splines on Uniform and Non-uniform Grids and Image Processing

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Order Approximation ◽  
Approximation Error ◽  
Polynomial Splines ◽  
Third Order ◽  
The Third ◽  
Uniform Grids ◽  
Trigonometric Splines ◽  
Image Enlargement ◽  
Third Order Approximation ◽  
Approximation Polynomial

This work is one of a series of papers that is devoted to the further investigation of polynomial splines and trigonometric splines of the third order approximation. Polynomial basis splines are better known and therefore more commonly used. However, the use of trigonometric basis splines often provides a smaller approximation error. In some cases, the use of the trigonometric approximations is preferable to the polynomial approximations. Here we continue to compare these two types of approximation. The Lebesgue functions and constants are discussed for the polynomial splines and the trigonometric splines. The examples of the applications of the splines to image enlargement are given.

MODULATION STABILITY OF WAVE PACKETS IN A THREE-LAYER HYDRODYNAMIC SYSTEM

2019 ◽  
pp. 30-35
Author(s):  
O. Avramenko ◽  
M. Lunyova
Keyword(s):  
Order Approximation ◽  
Wave Packets ◽  
Stability Diagram ◽  
Third Order ◽  
Weakly Nonlinear ◽  
The Third ◽  
Hydrodynamic System ◽  
Contact Surfaces ◽  
The Stability ◽  
Third Order Approximation

The article is devoted to the problem of propagation of weakly nonlinear wave-packets along contact surfaces in a three-layer hydrodynamic system "half space – layer – layer with rigid lid". The condition of solvability of the problem in the third-order approximation is obtained, the evolution equation is derived in the form of a nonlinear Schrodinger equation and the modulation stability condition for its solutions is obtained. The stability diagram and its analysis are presented for the solution which takes place in the case of the balance between dispersion and non-linearity.

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