Authors :
Md. Abdullah Bin Masud; Faijun Nesa Shimi; Rathindra Chandra Gope
Volume/Issue :
Volume 9 - 2024, Issue 9 - September
Google Scholar :
https://tinyurl.com/ys82959w
Scribd :
https://tinyurl.com/yjdjwdvx
DOI :
https://doi.org/10.38124/ijisrt/IJISRT24SEP1327
Note : A published paper may take 4-5 working days from the publication date to appear in PlumX Metrics, Semantic Scholar, and ResearchGate.
Abstract :
Numerical integration is a fundamental
concept in computational mathematics and plays a
crucial role in various scientific and engineering
disciplines. This paper provides a comprehensive review
of numerical integration techniques, their applications,
comparative analysis, and conclusions. The discussed
methods include the trapezoidal rule, Simpson’s rule,
Gaussian quadrature, and Widdle’s method methods.
The accuracy, efficiency, and limitations of each method
are evaluated through theoretical analysis and practical
examples.
Keywords :
Trapezoidal Rule, Simpson’s One Third Rule, Simpson’s Three Eight Rule, Widdles Rule, Gaussian Quadrature.
References :
- K. Ohta, H. Ishida, Comparison among several numerical integration methods for kramers-kronig transformation, Applied spectroscopy 42 (6) (1988) 952–957.
- R. Siushansian, J. LoVetri, A comparison of numerical techniques for modeling electromagnetic dispersive media, IEEE Microwave and Guided Wave Letters 5 (12) (1995) 426–428.
- E. Pennestr`ı, V. Rossi, P. Salvini, P. P. Valentini, Review and comparison of dry friction force models, Nonlinear dynamics 83 (2016) 1785– 1801.
- F. E. Uilhoorn, A comparison of numerical integration schemes for particle filter-based estimation of gas flow dynamics, Physica Scripta 93 (12) (2018) 125001.
- S. S. Bhonsale, D. Telen, B. Stokbroekx, J. Van Impe, Comparison of numerical solution strategies for population balance model of continuous cone mill, Powder technology 345 (2019) 739–749.
- M. C. Ausin, An introduction to quadrature and other numerical integration techniques (2007).
- R. K. Sinha, R. Kumar, Numerical method for evaluating the integrable function on a finite interval, International Journal of Engineering Science and Technology 2 (6) (2010) 2200–2206.
- Q. Docquier, O. Br¨uls, P. Fisette, Comparison and analysis of multibody dynamics formalisms for solving optimal control problem, in: IUTAM Symposium on Intelligent Multibody Systems–Dynamics, Control, Simulation, Springer, 2019, pp. 55–77.
- V. Parisi, R. Capuzzo-Dolcetta, A new method to integrate newtonian n-body dynamics, Journal of Physics A: Mathematical and Theoretical 52 (45) (2019) 454001.
- B. Brands, D. Davydov, J. Mergheim, P. Steinmann, Reduced-order modelling and homogenisation in magneto-mechanics: A numerical comparison of established hyper-reduction methods, Mathematical and Computational Applications 24 (1) (2019) 20.
Numerical integration is a fundamental
concept in computational mathematics and plays a
crucial role in various scientific and engineering
disciplines. This paper provides a comprehensive review
of numerical integration techniques, their applications,
comparative analysis, and conclusions. The discussed
methods include the trapezoidal rule, Simpson’s rule,
Gaussian quadrature, and Widdle’s method methods.
The accuracy, efficiency, and limitations of each method
are evaluated through theoretical analysis and practical
examples.
Keywords :
Trapezoidal Rule, Simpson’s One Third Rule, Simpson’s Three Eight Rule, Widdles Rule, Gaussian Quadrature.