A meshless method of lines using Lagrange interpolation polynomials for solving the coupled nonlinear sine-Gordon equations

2016 ◽  
Vol 11 ◽  
pp. 139-154
Author(s):  
T. Sarisahin ◽  
Y. Keskin ◽  
B.P. Allahverdiev
Keyword(s):  
Meshless Method ◽  
Lagrange Interpolation ◽  
Method Of Lines ◽  
Lagrange Interpolation Polynomials ◽  
Interpolation Polynomials ◽  
Meshless Method Of Lines

scholarly journals On Lagrange interpolation with equally spaced nodes

2000 ◽  
Vol 62 (3) ◽  
pp. 357-368 ◽  
Author(s):  
Michael Revers
Keyword(s):  
Rate Of Convergence ◽  
Lagrange Interpolation ◽  
End Points ◽  
Quantitative Version ◽  
Equidistant Nodes ◽  
Lagrange Interpolation Polynomials ◽  
Interpolation Polynomials ◽  
Exact Rate Of Convergence

A well-known result due to S.N. Bernstein is that sequence of Lagrange interpolation polynomials for |x| at equally spaced nodes in [−1, 1] diverges everywhere, except at zero and the end-points. In this paper we present a quantitative version concerning the divergence behaviour of the Lagrange interpolants for |x|3 at equidistant nodes. Furthermore, we present the exact rate of convergence for the interpolatory parabolas at the point zero.

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