scholarly journals A Spectral Transform Method for Singular Sturm--Liouville Problems with Applications to Energy Diffusion in Plasma Physics

2015 ◽  
Vol 75 (2) ◽  
pp. 350-392 ◽  
Author(s):  
Jon Wilkening ◽  
Antoine Cerfon
Keyword(s):  
Plasma Physics ◽  
Transform Method ◽  
Energy Diffusion ◽  
Spectral Transform ◽  
Sturm Liouville

Numerical simulation for coupled nonlinear Schrödinger–Korteweg–de Vries and Maccari systems of equations

2021 ◽  
pp. 2150339
Author(s):  
Lanre Akinyemi ◽  
Pundikala Veeresha ◽  
Samuel Oluwatosin Ajibola
Keyword(s):  
Numerical Simulation ◽  
Plasma Physics ◽  
Acoustic Waves ◽  
Electromagnetic Waves ◽  
Nonlinear Partial Differential Equations ◽  
Transform Method ◽  
Langmuir Waves ◽  
Suggested Approach ◽  
Nonlinear Schrödinger ◽  
De Vries

The primary goal of this paper is to seek solutions to the coupled nonlinear partial differential equations (CNPDEs) by the use of q-homotopy analysis transform method (q-HATM). The CNPDEs considered are the coupled nonlinear Schrödinger–Korteweg–de Vries (CNLS-KdV) and the coupled nonlinear Maccari (CNLM) systems. As a basis for explaining the interactive wave propagation of electromagnetic waves in plasma physics, Langmuir waves and dust-acoustic waves, the CNLS-KdV model has emerged as a model for defining various types of wave phenomena in mathematical physics, and so forth. The CNLM model is a nonlinear system that explains the dynamics of isolated waves, restricted in a small part of space, in several fields like nonlinear optics, hydrodynamic and plasma physics. We construct the solutions (bright soliton) of these models through q-HATM and present the numerical simulation in form of plots and tables. The solutions obtained by the suggested approach are provided in a refined converging series. The outcomes confirm that the proposed solutions procedure is highly methodological, accurate and easy to study CNPDEs.

Parallelizing the spectral transform method

1992 ◽  
Vol 4 (4) ◽  
pp. 269-291 ◽  
Author(s):  
Patrick H. Worley ◽  
John B. Drake
Keyword(s):  
Transform Method ◽  
Spectral Transform

scholarly journals Numerical integration of the axisymmetric Robinson-Trautman equation by a spectral method

1999 ◽  
Vol 41 (2) ◽  
pp. 271-280 ◽  
Author(s):  
D. A. Prager ◽  
A. W.-C. Lun
Keyword(s):  
Numerical Integration ◽  
Spectral Decomposition ◽  
Finite Difference Schemes ◽  
Qualitative Comparison ◽  
Transform Method ◽  
Higher Order Modes ◽  
Spectral Transform ◽  
Long Time ◽  
Bondi Mass ◽  
Meteorological Problems

AbstractWe have adapted the Spectral Transform Method, a technique commonly used in non-linear meteorological problems, to the numerical integration of the Robinson-Trautman equation. This approach eliminates difficulties due to the S2 × R+ topology of the equation. The method is highly accurate for smooth data and is numerically robust. Under spectral decomposition the long-time equilibrium state takes a particularly simple form: all nonlinear (l ≥ 2) modes tend to zero. We discuss the interaction and eventual decay of these higher order modes, as well as the evolution of the Bondi mass and other derived quantities. A qualitative comparison between the Spectral Transform Method and two finite difference schemes is given.

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