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A numerical integration approach by weight factors and its accuracy
Author(s) -
Mihailović Vojislav
Publication year - 1989
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620280515
Subject(s) - mathematics , numerical integration , simple (philosophy) , gaussian , mathematical analysis , calculus (dental) , physics , medicine , philosophy , dentistry , epistemology , quantum mechanics
A new parabolic approach for numerical integration using weight coefficients is proposed. Several basic approaches for integration have been analysed: linear (trapezoidal), parabolic (new form), Simpson's, Newton–Cotes and Gaussian. The weight coefficients are transformed into the same form for all methods. Simpson's and Newton's formulas (for n = 3) are obtained as special cases of the general parabolic formula. A simple procedure to estimate the accuracy of the integral for final intervals is given.