Accurate Evaluation Schemes for Triangular Domain Integrals

𝑛(𝑛 +1) 2 -1 points (for n >1) Gaussian quadrature formulae for triangle utilizing n-point one-dimensional Gaussian quadrature.By use of simple but straight-forward algorithms, Gaussian points and corresponding weights are calculated and presented for clarity and reference.The proposed 𝑛(𝑛+1) 2 -1 point formula completely avoids the crowding of Gaussian points.Finally, it presents an error formula which can evaluate the error in monomial/polynomial integration using m×n point method successfully.The error calculated by the new formula and the error in calculation of integrals by the proposed methods are found to be in good agreement.Thus, it overcomes all the drawbacks in view of accuracy and efficiency for the numerical evaluation of the triangular domain integrals of any arbitrary functions encountered in the realm of science and engineering.