Title: Numerical Differentiation and Integration through Aitken-Neville Schemes
Author(s): Ramesh Kumar Muthumalai
Pages: 104-111
Cite as:
Ramesh Kumar Muthumalai, Numerical Differentiation and Integration through Aitken-Neville Schemes, Int. J. Anal. Appl., 3 (2) (2013), 104-111.

Abstract


Some new formulas are given to approximate higher order derivatives and integrals through Aitken-Neville iterative schemes for arbitrary spaced grids. An algorithm is given in MATLAB for numerical differentiation. Also, numerical examples are provided to study error analysis of new formulas for numerical differentiation and integration.

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References


  1. K. E. Atkinson, An introdction to numerical Analysis, 2 Ed, John Wiley & Sons, Newyork (1989). Google Scholar

  2. S.D. Conte, Carl de boor, Elementary numerical Analysis, 3 Ed, McGraw-Hill, Newyork, USA (1980). Google Scholar

  3. M. Dvornikov, Formulae for Numerical differentiation, JCAAM, 5 (2007), 77-88 [e-print arxiv:math.NA/0306092]. Google Scholar

  4. B. Fornberg, Calculation of weights in finite difference formulas, SIAM Rev, Vol 40, No 3, 685-691 (1998). Google Scholar

  5. F.B. Hildebrand, Introduction to Numerical analysis, 2 Ed, McGraw-Hill, Newyork (1974). Google Scholar

  6. J.Li, General Explicit difference formulas for Numerical differentiation, J.Comp & Appl. Math, 183, 29-52 (2005). Google Scholar

  7. G. M. Phillips, Interpolation and approximation by polynomials, Springer-Verlag, Newyork (2003). Google Scholar

  8. S.S. Sastry, Introdutory methods of Numerical Analysis, 4 Ed, Prentice hall of India, New Delhi (2005). Google Scholar

  9. E. S¨uli & D. Mayers, An introduction to Numerical Analysis, Cambridge University Press, UK (2003). Google Scholar