New symmetric interpolatory quadrature formulas

CALCOLO ◽  
1995 ◽  
Vol 32 (1-2) ◽  
pp. 39-50
Author(s):  
P. Favati ◽  
G. Lotti ◽  
F. Romani
Keyword(s):  
Quadrature Formulas ◽  
Interpolatory Quadrature

Theoretical and practical efficiency measures for symmetric interpolatory quadrature formulas

1994 ◽  
Vol 34 (4) ◽  
pp. 546-557 ◽  
Author(s):  
Paola Favati ◽  
Grazia Lotti ◽  
Francesco Romani
Keyword(s):  
Quadrature Formulas ◽  
Efficiency Measures ◽  
Interpolatory Quadrature

scholarly journals Positive rational interpolatory quadrature formulas on the unit circle and the interval

2010 ◽  
Vol 60 (12) ◽  
pp. 1286-1299 ◽  
Author(s):  
Karl Deckers ◽  
Adhemar Bultheel ◽  
Ruymán Cruz-Barroso ◽  
Francisco Perdomo-Pío
Keyword(s):  
Unit Circle ◽  
Quadrature Formulas ◽  
Interpolatory Quadrature

scholarly journals Positive interpolatory quadrature formulas and para-orthogonal polynomials

2005 ◽  
Vol 179 (1-2) ◽  
pp. 97-119 ◽  
Author(s):  
Adhemar Bultheel ◽  
Leyla Daruis ◽  
Pablo González-Vera
Keyword(s):  
Orthogonal Polynomials ◽  
Quadrature Formulas ◽  
Interpolatory Quadrature

On Quadrature Formulas

2018 ◽  
Vol 481 (2) ◽  
pp. 136-137
Author(s):  
V. Chubarikov ◽  
Keyword(s):  
Quadrature Formulas

scholarly journals Collocation Methods for High-Order Well-Balanced Methods for Systems of Balance Laws

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1799
Author(s):  
Irene Gómez-Bueno ◽  
Manuel Jesús Castro Díaz ◽  
Carlos Parés ◽  
Giovanni Russo
Keyword(s):  
High Order ◽  
Collocation Methods ◽  
Quadrature Formulas ◽  
Balance Laws ◽  
Source Terms ◽  
Time Step ◽  
Systems Of Balance Laws ◽  
Reconstruction Operator ◽  
Non Linear ◽  
Linear Problems

In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced reconstruction operator. Moreover, they introduced a procedure to modify any standard reconstruction operator, like MUSCL, ENO, CWENO, etc., in order to be well-balanced. This strategy involves a non-linear problem at every cell at every time step that consists in finding the stationary solution whose average is the given cell value. In a recent paper, a fully well-balanced method is presented where the non-linear problems to be solved in the reconstruction procedure are interpreted as control problems. The goal of this paper is to introduce a new technique to solve these local non-linear problems based on the application of the collocation RK methods. Special care is put to analyze the effects of computing the averages and the source terms using quadrature formulas. A general technique which allows us to deal with resonant problems is also introduced. To check the efficiency of the methods and their well-balance property, they have been applied to a number of tests, ranging from easy academic systems of balance laws consisting of Burgers equation with some non-linear source terms to the shallow water equations—without and with Manning friction—or Euler equations of gas dynamics with gravity effects.

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