Error of Approximation in Case of Definite Integrals

Full Text(PDF, 3000) PP.


Author(s) 
Rajesh Kumar Sinha, Satya Narayan Mahto, Dhananjay Sharan 

KEYWORDS 
Quadrature rule, Simpsons rule, Chebyshev polynomials, approximation, interpolation, error.


ABSTRACT 
This paper proposes a method for computation of error of approximation involved in case of evaluation of integrals of single variable. The error associated with a quadrature rule provides information with a difference of approximation. In numerical integration, approximation of any function is done through polynomial of suitable degree but shows a difference in their integration integrated over some interval. Such difference is error of approximation. Sometime, it is difficult to evaluate the integral by analytical methods Numerical Integration or Numerical Quadrature can be an alternative approach to solve such problems. As in other numerical techniques, it often results in approximate solution. The Integration can be performed on a continuous function on set of data.


References 

[1] K. E. Atkinson, An Introduction to Numerical Analysis, Wiley,
NewYork, 1993.
[2] R. E. Beard, “Some notes on approximate product integration,”
J. Inst. Actur., vol. 73, pp. 356416, 1947.
[3] C. T. H. Baker, “On the nature of certain quadrature formulas
and their errors,” SIAM. J. Numer anal., vol. 5, pp. 783804, 1968.
[4] P. J. Daniell, “Remainders in interpolation and quadrature formulae,”
Math. Gaz., Vol. 24, pp. 238244, 1940.
[5] R. K. Sinha, “Estimating error involved in case of Evaluation of
Integrals of single variable,” Int J. Comp. Tech. Appl., Vol. 2, No.
2, pp. 345348, 2011.
[6] T. J. Akai, Applied Numerical Methods for Engineerrs, Wiley,
NewYok, 1993.
[7] L. M. Delves, “The Numerical Evaluation of Principal Value
Integrals,” Computer Journal, Vol. 10, pp. 389, 1968.
[8] Brain Bradi, A Friendly Introduction to Numerical Analysis,
pp. 441532, Pearson Education, 2009.
[9] R. K. Sinha, “Numerical Method for evaluating the Integrable
function on a finite interval,” Int. J. of Engineering Science and
Technology, Vol. 2, No. 6, pp. 22002206, 2010.
[10] C. E. Froberg, Introduction to Numerical Analysis, Addison
Wesley Pub. Co. Inc.
[11] Ibid, The Numerical Evaluation of class Integrals, Proc. Comb.
Phil. Soc.52.
[12] P .J .Davis and P. Rebinowitz, Method of Numerical Integration,
2nd edition, Academic Press, New York, 1984.


