A High-Order Finite-Difference Scheme with a Linearization Technique for Numerical Solution of Two Dimensional Burgers Equation

2016 ◽  
Vol 40 (5) ◽  
pp. 306-312
Author(s):  
Marco Donisete de Campos ◽  
◽  
Estaner Claro Romão
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Finite Difference Scheme ◽  
Burgers Equation ◽  
High Order ◽  
Two Dimensional ◽  
Linearization Technique ◽  
High Order Finite Difference

Analyses of the Dispersion Overshoot and Inverse Dissipation of the High-Order Finite Difference Scheme

2013 ◽  
Vol 5 (06) ◽  
pp. 809-824 ◽  
Author(s):  
Qin Li ◽  
Qilong Guo ◽  
Hanxin Zhang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
High Order ◽  
Staggered Grid ◽  
Third Order ◽  
Order Scheme ◽  
Relationship Of ◽  
High Order Finite Difference ◽  
The Relationship

AbstractAnalyses were performed on the dispersion overshoot and inverse dissipation of the high-order finite difference scheme using Fourier and precision analysis. Schemes under discussion included the pointwise- and staggered-grid type, and were presented in weighted form using candidate schemes with third-order accuracy and three-point stencil. All of these were commonly used in the construction of difference schemes. Criteria for the dispersion overshoot were presented and their critical states were discussed. Two kinds of instabilities were studied due to inverse dissipation, especially those that occur at lower wave numbers. Criteria for the occurrence were presented and the relationship of the two instabilities was discussed. Comparisons were made between the analytical results and the dispersion/dissipation relations by Fourier transformation of typical schemes. As an example, an application of the criteria was given for the remedy of inverse dissipation in Weirs & Martín’s third-order scheme.

scholarly journals Hot Electron Modelling of HEMTs

VLSI Design ◽  
2001 ◽  
Vol 13 (1-4) ◽  
pp. 287-293 ◽  
Author(s):  
Eric A. B. Cole ◽  
Christopher M. Snowden ◽  
Shahzad Hussain
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Quantum Wells ◽  
Numerical Solution ◽  
Conduction Band ◽  
Finite Difference Scheme ◽  
Energy Transport ◽  
Two Dimensional ◽  
Hot Electron ◽  
Recessed Gate

The hot-electron two-dimensional HEMT with recessed gate is modelled by solving the Poisson, current continuity and energy transport equations consistently with the Schrödinger equation using a finite difference scheme. New expressions are used for the energy densities inside and outside the quantum wells. A method is described for pinning the conduction band at the contact edge to produce an extremely stable numerical solution. Results are presented for an eight layer GaAs-ALGaAs-InGaAs device.

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