PDEX1M — A Software Package for the Numerical Solution of Parabolic Systems in One Space Dimension

1996 ◽  
pp. 163-169
Author(s):  
U. Nowak
Keyword(s):  
Numerical Solution ◽  
Software Package ◽  
Space Dimension ◽  
Parabolic Systems ◽  
One Space Dimension

Convergence of diffusive BGK approximations for nonlinear strongly parabolic systems

2002 ◽  
Vol 132 (2) ◽  
pp. 341-358 ◽  
Author(s):  
Corrado Lattanzio ◽  
Roberto Natalini
Keyword(s):  
Space Dimension ◽  
Global Solutions ◽  
Parabolic Systems ◽  
Compensated Compactness ◽  
Rigorous Result ◽  
Formal Limit ◽  
One Space Dimension

We study a class of BGK approximations of parabolic systems in one space dimension. We prove stability and existence of global solutions for this model. Moreover, under certain conditions, we prove a rigorous result of convergence toward the formal limit, by using compensated compactness techniques.

On the construction of orthogonal curvilinear grids for regional oceanic modeling: algorithm and user guide

2020 ◽  
Vol 48 (4) ◽  
pp. 45-111
Author(s):  
A. F. Shepetkin
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
Elliptic Problem ◽  
Software Package ◽  
Conformal Transformation ◽  
Iterative Procedure ◽  
Geometric Shape ◽  
Curvilinear Grids ◽  
Grid Points ◽  
Grid Nodes

A new algorithm for constructing orthogonal curvilinear grids on a sphere for a fairly general geometric shape of the modeling region is implemented as a “compile-once - use forever” software package. It is based on the numerical solution of the inverse problem by an iterative procedure -- finding such distribution of grid points along its perimeter, so that the conformal transformation of the perimeter into a rectangle turns this distribution into uniform one. The iterative procedure itself turns out to be multilevel - i.e. an iterative loop built around another, internal iterative procedure. Thereafter, knowing this distribution, the grid nodes inside the region are obtained solving an elliptic problem. It is shown that it was possible to obtain the exact orthogonality of the perimeter at the corners of the grid, to achieve very small, previously unattainable level of orthogonality errors, as well as make it isotropic -- local distances between grid nodes about both directions are equal to each other.

scholarly journals Self-adjoint Dirac type Hamiltonians in one space dimension with a mass jump

2015 ◽  
Vol 48 (4) ◽  
pp. 045207 ◽  
Author(s):  
L A González-Díaz ◽  
Alberto A Díaz ◽  
S Díaz-Solórzano ◽  
J R Darias
Keyword(s):  
Space Dimension ◽  
Dirac Type ◽  
One Space Dimension
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