Fundamental Aspects of Numerical Methods for the Propagation of Multi-Dimensional Nonlinear Waves in Solids

1989 ◽  
pp. 574-588 ◽  
Author(s):  
M. Staat ◽  
J. Ballmann
Keyword(s):  
Numerical Methods ◽  
Nonlinear Waves

Dynamics of waves and multidimensional solitons of the Zakharov–Kuznetsov equation

2000 ◽  
Vol 64 (4) ◽  
pp. 397-409 ◽  
Author(s):  
E. INFELD ◽  
A. A. SKORUPSKI ◽  
A. SENATORSKI
Keyword(s):  
Numerical Methods ◽  
Nonlinear Wave ◽  
Parameter Space ◽  
Growth Rates ◽  
Nonlinear Waves ◽  
Wave Length ◽  
Two Dimensions ◽  
One Dimensional

Nonlinear waves and one-dimensional solitons of the Zakharov–Kuznetsov equation are unstable in two dimensions. Although the wavevector K of a perturbation leading to an instability covers a whole region in (Kx, Ky) parameter space, two classes are of particular interest. One corresponds to the perpendicular, Benjamin–Feir instability (Kx = 0). The second is the wave-length-doubling instability. These two are the only purely growing modes. We concentrate on them. Both analytical and numerical methods for calculating growth rates are employed and results compared. Once a nonlinear wave or soliton breaks up owing to one of these instabilities, an array of cylindrical and/or spherical solitons can emerge. We investigate the interaction of these entities numerically.

Numerical Methods

2019 ◽  
Author(s):  
Rajesh Kumar Gupta
Keyword(s):  
Numerical Methods

Nonlinear Waves, Solitons and Chaos

2000 ◽  
Author(s):  
Eryk Infeld ◽  
George Rowlands
Keyword(s):  
Nonlinear Waves

THE METHODS OF DEVELOPING COMPUTATIONAL THINKING OF STUDENTS WHILE STUDYING THE COURSE "NUMERICAL METHODS" BASED ON BLENDED LEARNING

2019 ◽  
pp. 34-41
Author(s):  
M. M. Klunnikova
Keyword(s):  
Numerical Methods ◽  
Blended Learning ◽  
Computational Thinking ◽  
Individual Characteristics ◽  
Diagnostic Model ◽  
Mathematics Students ◽  
Professional Activities ◽  
Cognitive Component ◽  
Professional Field ◽  
The Individual

The work is devoted to the consideration of improving the quality of teaching students the discipline “Numerical methods” through the development of the cognitive component of computational thinking based on blended learning. The article presents a methodology for the formation of computational thinking of mathematics students, based on the visualization of algorithmic design schemes and the activation of the cognitive independence of students. The characteristic of computational thinking is given, the content and structure of computational thinking are shown. It is argued that a student with such a mind is able to manifest himself in his professional field in the best possible way. The results of the application of the technique are described. To determine the level of development of the cognitive component of computational thinking, a diagnostic model has been developed based on measuring the content, operational and motivational components. It is shown that the proposed method of developing computational thinking of students, taking into account the individual characteristics of students’ thinking, meaningfully based on the theoretical and practical aspects of studying the discipline, increases the effectiveness of learning the course “Numerical methods”. The materials of the article are of practical value for teachers of mathematical disciplines who use information and telecommunication technologies in their professional activities.

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