A Generalized Barycentric Rational Interpolation Method for Generalized Abel Integral Equations

2020 ◽  
Vol 6 (5) ◽  
Author(s):  
H. Azin ◽  
F. Mohammadi ◽  
D. Baleanu
Keyword(s):  
Integral Equations ◽  
Interpolation Method ◽  
Rational Interpolation ◽  
Abel Integral Equations ◽  
Barycentric Rational Interpolation

scholarly journals Linear Barycentric Rational Method for Solving Schrodinger Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Peichen Zhao ◽  
Yongling Cheng
Keyword(s):  
Schrödinger Equation ◽  
Convergence Rate ◽  
Collocation Method ◽  
Schrodinger Equation ◽  
Interpolation Method ◽  
Rational Interpolation ◽  
Barycentric Interpolation ◽  
Rational Polynomial ◽  
The Matrix ◽  
Barycentric Rational Interpolation

A linear barycentric rational collocation method (LBRCM) for solving Schrodinger equation (SDE) is proposed. According to the barycentric interpolation method (BIM) of rational polynomial and Chebyshev polynomial, the matrix form of the collocation method (CM) that is easy to program is obtained. The convergence rate of the LBRCM for solving the Schrodinger equation is proved from the convergence rate of linear barycentric rational interpolation. Finally, a numerical example verifies the correctness of the theoretical analysis.

scholarly journals A family of methods for Abel integral equations of the second kind

1991 ◽  
Vol 34 (2) ◽  
pp. 211-219 ◽  
Author(s):  
H. Brunner ◽  
M.R. Crisci ◽  
E. Russo ◽  
A. Vecchio
Keyword(s):  
Integral Equations ◽  
Abel Integral Equations

scholarly journals The barycentric rational interpolation collocation method for boundary value problems

2018 ◽  
Vol 22 (4) ◽  
pp. 1773-1779 ◽  
Author(s):  
Dan Tian ◽  
Ji-Huan He
Keyword(s):  
Boundary Value Problems ◽  
Collocation Method ◽  
Analytical Methods ◽  
Boundary Value ◽  
Rational Interpolation ◽  
Higher Order ◽  
Barycentric Rational Interpolation

Higher-order boundary value problems have been widely studied in thermal science, though there are some analytical methods available for such problems, the barycentric rational interpolation collocation method is proved in this paper to be the most effective as shown in three examples.

Systems of Generalized Abel Integral Equations.

1977 ◽  
Author(s):  
M. Lowengrub ◽  
J. R. Walton
Keyword(s):  
Integral Equations ◽  
Abel Integral Equations

Abel Integral Equations

1990 ◽  
pp. 373-410 ◽  
Author(s):  
R. S. Anderssen ◽  
F. R. Hoog
Keyword(s):  
Integral Equations ◽  
Abel Integral Equations
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