1. Key Laboratory of Metallogenic Prediction of Nonferrous Metals, Ministry of Education, School of Geosciences and Info-Physics, Central South University, Changsha 410083, China;
2. School of Mathematical Sciences and Computing Technology, Central South University, Changsha 410075, China;
3. HPCSIP Key Laboratory, Ministry of Education, Changsha 410081, China;
4. Department of Mathematics, Shanghai University, Shanghai 200444
Based on the remainder term for Gauss-Legendre quadrature rule, the corresponding correction formulas for numerical integral is proposed, and extended to the calculation of multiple integrals. It is proved that correction formula increases the algebraic accuracy at least two-order. Numerical experiments show that the correction formulas has higher accuracy than the original formulas, can quickly converge to the exact value of the integral. Thus it is of great use in many engineering applications.
Rathod H T, Venkatesudu B, Nagaraja K V. On the application of two Gauss-Legendre quadraturerules for composite numerical integration over a tetrahedral region[J]. Appl. Math. Comput., 2007,189(1): 131-162
Reddy C T, Shippy D J. Alternative integration formulae for triangular finite elements[J]. Int. J.Numer. Meth. Eng., 1981, 17(1): 133-153.