Bulletin of Pure & Applied Sciences- Mathematics and Statistics
  • Year: 2018
  • Volume: 37e
  • Issue: 2

Use of mixed cubature rule for evaluation of integrals over triangular region in adaptive environment

1Department of Mathematics, Ravenshaw University, Cuttack-753003, Odisha, India E-mail: pritikanta@yahoo.com

2Department of Mathematics, Ravenshaw University, Cuttack-753003, Odisha, India E-mail: debasisdas100@gmail.com

3Department of Mathematics, Ravenshaw University, Cuttack-753003, Odisha, India E-mail: rajanibdash@rediffmail.com

*Corresponding Author: Rajani Ballav Dash, Department of Mathematics, Ravenshaw University, Cuttack-753003, Odisha, India, E-mail: rajanibdash@rediffmail.com

Mathematics Subject Classification: 65D30, 65D32

Abstract

A new mixed cubature rule is established for 2-simplexes (i.e., triangles). Extending anti-Gauss 3-point rule and Fejer's second 3-point rule in two dimensions and then combining those the mixed cubature rule is formed which is of precision 5. Also an adaptive cubature algorithm is devised to boost up the mixed cubature rule. Some test integrals are also numerically evaluated to show the efficiency of the mixed rule in adaptive environment.

Keywords

Anti-Gauss 3-point rule {R2aG3 (f)}, Fejer's second 3-point rule {R22F3 (f)}, mixed cubature rule {R2aG3f3 (f)}, open type cubature rule, adaptive cubature routine, triangular domain