An explicit higher order difference scheme on a compact stencil for elliptic equations on curvilinear geometries

2014 ◽  
Vol 242 ◽  
pp. 143-158
Author(s):  
K. Asthana ◽  
T.K. Sengupta
Keyword(s):  
Difference Scheme ◽  
Elliptic Equations ◽  
Higher Order ◽  
Order Difference ◽  
Compact Stencil

scholarly journals A higher-order difference scheme of the Cabaret class for solving the transport equation

2018 ◽  
pp. 185-193
Author(s):  
А.В. Соловьев ◽  
А.В. Данилин
Keyword(s):  
Difference Scheme ◽  
Transport Equation ◽  
Higher Order ◽  
Scalar Transport ◽  
Order Of Approximation ◽  
Order Of Accuracy ◽  
Order Difference ◽  
Cabaret Scheme ◽  
Dispersion Properties

Предложена новая разностная схема класса Кабаре повышенного порядка точности для решения скалярного уравнения переноса. Порядок аппроксимации разностной схемы равен четырем. Построено балансно-характеристическое представление схемы и приведены дисперсионные свойства. Для предложенной разностной схемы в сравнении с классической схемой Кабаре рассмотрены примеры решения уравнения переноса для гладкого и разрывного профиля. A new difference scheme of the Cabaret class with a higher order of accuracy for solving the scalar transport equation is proposed. The order of approximation of this difference scheme is equal to four. The balance-characteristic representation of the scheme is constructed and the dispersion properties are given. For the proposed difference scheme, a number of examples to solve the transport equation for smooth and discontinuous profiles are considered in comparison with the classical Cabaret scheme.

scholarly journals An infinite family of higher-order difference operators that commute with Ruijsenaars operators of type A

2021 ◽  
Vol 111 (4) ◽  
Author(s):  
Masatoshi Noumi ◽  
Ayako Sano
Keyword(s):  
Infinite Family ◽  
Type A ◽  
Higher Order ◽  
Difference Operators ◽  
Order Difference

AbstractWe introduce a new infinite family of higher-order difference operators that commute with the elliptic Ruijsenaars difference operators of type A. These operators are related to Ruijsenaars’ operators through a formula of Wronski type.

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