Numerical solution of many integral transforms using Gauss Legendre Quadrature rules mainly resulted in ill conditioned system of nonlinear equations. In some recent works in numerical improvement of integrals new nodes and weights are applied to improve the solution. The main problem in these approaches is still available, in this paper we use a new modified form of Gauss Legendre Quadrature rules and determine the nodes and weights such that minimize the error of integration. This determination reduces to a system of nonlinear equations with some irregular conditions due to the ill-conditioned matrices. We have presented an explicit solution to the fast calculation of inversion of the matrix. Finally, we compare the results with exact solutions to see the improvement.
|Journal||International Journal of Mathematics and Computation|
|Publication status||Published - 2011|