Application of MATLAB Symbolic Maths with Variable Precision Arithmetic (VPA) to Compute Some High Order Gauss Legendre Quadrature Rules

Authors

  • HT Rathod Department of Mathematics, Central college campus, Bangalore University, Bangalore
  • RD Sathish Department of Mathematics, Vijaya Degree college, R.V. Road, Bangalore
  • Md Shafiqul Islam Department of Mathematics, University of Dhaka, Dhaka
  • Arun Kumar Gali Department of Mathematics, Acharya Institute of Technology, Bangalore

DOI:

https://doi.org/10.3329/ganit.v29i0.8521

Keywords:

MATLAB, Gauss Legendre Quadrature Rules

Abstract

Gauss Legendre Quadrature rules are extremely accurate and they should be considered seriously when many integrals of similar nature are to be evaluated. This paper is concerned with the derivation and computation of numerical integration rules for the three integrals: (See text for formulae)

which are dependent on the zeros and the squares of the zeros of Legendre Polynomial and is quite well known in the Gaussian Quadrature theory. We have developed the necessary MATLAB programs based on symbolic maths which can compute the sampling points and the weight coefficients and are reported here upto 32 – digits accuracy and we believe that they are reported to this accuracy for the first time. The MATLAB programs appended here are based on symbolic maths. They are very sophisticated and they can compute Quadrature rules of high order, whereas one of the recent MATLAB program appearing in reference [21] can compute Gauss Legendre Quadrature rules upto order twenty, because the zeros of Legendre polynomials cannot be computed to desired accuracy by MATLAB routine roots (……..). Whereas we have used the MATLAB routine solve (……..) to find zeros of polynomials which is very efficient. This is worth noting in the present context.

GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 29 (2009) 117-125 

DOI: http://dx.doi.org/10.3329/ganit.v29i0.8521 

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How to Cite

Rathod, H., Sathish, R., Islam, M. S., & Gali, A. K. (2011). Application of MATLAB Symbolic Maths with Variable Precision Arithmetic (VPA) to Compute Some High Order Gauss Legendre Quadrature Rules. GANIT: Journal of Bangladesh Mathematical Society, 29, 117–125. https://doi.org/10.3329/ganit.v29i0.8521

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