Application of CAS wavelet to construct quadrature rules for numerical ‎integration‎‎

Subject Areas : International Journal of Industrial Mathematics

S. Rezabeyk ¹ , KH. Maleknejad ²

1 - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
2 - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.

Received: 2015-02-03 Accepted : 2015-02-03 Published : 2015-01-01

Keywords: CAS Wavelets, Quadrature rules, Hybrid functions, Double and triple ‎integrals.‎,

Abstract :

In this paper‎, ‎based on CAS wavelets we present quadrature rules for numerical solution‎ ‎of double and triple integrals with variable limits of integration‎. ‎To construct new method‎, ‎first‎, ‎we approximate the unknown function by CAS wavelets‎. ‎Then by using suitable collocation points‎, ‎we obtain the CAS wavelet coefficients that these coefficients are applied in approximating the unknown function‎. ‎The major advantage of new approach is that this method can approximate the value of some improper integrals‎. ‎To illustrate the efficiency and the accuracy of the method‎, ‎some numerical examples are given.‎‎‎