On uniform difference schemes of a high order of approximation for evolution equations with a small parameter

1989 ◽  
Vol 10 (5-6) ◽  
pp. 593-606 ◽  
Author(s):  
Allaberen Ashyralyev
Keyword(s):  
Small Parameter ◽  
Evolution Equations ◽  
High Order ◽  
Difference Schemes ◽  
Order Of Approximation

scholarly journals Accurate Spectral Collocation Computations of High Order Eigenvalues for Singular Schrödinger Equations-Revisited

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 761
Author(s):  
Călin-Ioan Gheorghiu
Keyword(s):  
Schrödinger Equation ◽  
Small Parameter ◽  
Error Estimation ◽  
Schrodinger Equation ◽  
Error Control ◽  
High Order ◽  
Order Of Approximation ◽  
Schrödinger Equations ◽  
Spectral Collocation ◽  
Integration Interval

In this paper, we continue to solve as accurately as possible singular eigenvalues problems attached to the Schrödinger equation. We use the conventional ChC and SiC as well as Chebfun. In order to quantify the accuracy of our outcomes, we use the drift with respect to some parameters, i.e., the order of approximation N, the length of integration interval X, or a small parameter ε, of a set of eigenvalues of interest. The deficiency of orthogonality of eigenvectors, which approximate eigenfunctions, is also an indication of the accuracy of the computations. The drift of eigenvalues provides an error estimation and, from that, one can achieve an error control. In both situations, conventional spectral collocation or Chebfun, the computing codes are simple and very efficient. An example for each such code is displayed so that it can be used. An extension to a 2D problem is also considered.

On Convergence of High Order Shock Capturing Difference Schemes

2010 ◽  
Author(s):  
V. Ostapenko ◽  
Michail D. Todorov ◽  
Christo I. Christov
Keyword(s):  
High Order ◽  
Difference Schemes ◽  
Shock Capturing

A new family of high-order compact upwind difference schemes with good spectral resolution

2007 ◽  
Vol 227 (2) ◽  
pp. 1306-1339 ◽  
Author(s):  
Qiang Zhou ◽  
Zhaohui Yao ◽  
Feng He ◽  
M.Y. Shen
Keyword(s):  
Spectral Resolution ◽  
High Order ◽  
Difference Schemes ◽  
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