Uniform convergence of derivatives of extended Lagrange interpolation

1991 ◽  
Vol 60 (1) ◽  
pp. 195-218 ◽  
Author(s):  
Giuliana Criscuolo ◽  
Giuseppe Mastroianni ◽  
Donatella Occorsio
Keyword(s):  
Uniform Convergence ◽  
Lagrange Interpolation ◽  
Derivatives Of

scholarly journals Mean convergence of derivatives of Lagrange interpolation

1991 ◽  
Vol 34 (3) ◽  
pp. 385-396 ◽  
Author(s):  
Giuseppe Mastroianni ◽  
Paul Nevai
Keyword(s):  
Lagrange Interpolation ◽  
Mean Convergence ◽  
Derivatives Of

scholarly journals Multivariate Lagrange Interpolation at Sinc Points Error Estimation and Lebesgue Constant

2016 ◽  
Vol 8 (4) ◽  
pp. 118 ◽  
Author(s):  
Maha Youssef ◽  
Hany A. El-Sharkawy ◽  
Gerd Baumann
Keyword(s):  
Uniform Convergence ◽  
Error Estimation ◽  
Upper Bound ◽  
Lagrange Interpolation ◽  
Lebesgue Constant ◽  
Explicit Construction ◽  
Interpolation Operator ◽  
Lebesgue Constants ◽  
Set Of Points

This paper gives an explicit construction of multivariate Lagrange interpolation at Sinc points. A nested operator formula for Lagrange interpolation over an $m$-dimensional region is introduced. For the nested Lagrange interpolation, a proof of the upper bound of the error is given showing that the error has an exponentially decaying behavior. For the uniform convergence the growth of the associated norms of the interpolation operator, i.e., the Lebesgue constant has to be taken into consideration. It turns out that this growth is of logarithmic nature $O((log n)^m)$. We compare the obtained Lebesgue constant bound with other well known bounds for Lebesgue constants using different set of points.

Uniform convergence of lagrange interpolation processes

1986 ◽  
Vol 39 (2) ◽  
pp. 124-133
Author(s):  
A. A. Privalov
Keyword(s):  
Uniform Convergence ◽  
Lagrange Interpolation

scholarly journals Numerical Solutions of Fractional Differential Equations by Using Fractional Explicit Adams Method

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1675
Author(s):  
Nur Amirah Zabidi ◽  
Zanariah Abdul Majid ◽  
Adem Kilicman ◽  
Faranak Rabiei
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lagrange Interpolation ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Multistep Method ◽  
Stability And Convergence ◽  
Third Order ◽  
Fractional Differential ◽  
Derivatives Of

Differential equations of fractional order are believed to be more challenging to compute compared to the integer-order differential equations due to its arbitrary properties. This study proposes a multistep method to solve fractional differential equations. The method is derived based on the concept of a third-order Adam–Bashforth numerical scheme by implementing Lagrange interpolation for fractional case, where the fractional derivatives are defined in the Caputo sense. Furthermore, the study includes a discussion on stability and convergence analysis of the method. Several numerical examples are also provided in order to validate the reliability and efficiency of the proposed method. The examples in this study cover solving linear and nonlinear fractional differential equations for the case of both single order as α∈(0,1) and higher order, α∈1,2, where α denotes the order of fractional derivatives of Dαy(t). The comparison in terms of accuracy between the proposed method and other existing methods demonstrate that the proposed method gives competitive performance as the existing methods.

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