scholarly journals The Periodicity of the Accuracy of Numerical Integration Methods for the Solution of Different Engineering Problems

2021 ◽  
Author(s):  
Toukir Ahmed Chowdhury ◽  
Towhedul Islam ◽  
Ahmad Abdullah Mujahid ◽  
Md. Bayazid Ahmed
Keyword(s):  
Integral Equation ◽  
Numerical Integration ◽  
Integral Equations ◽  
Trapezoidal Rule ◽  
Integration Methods ◽  
Engineering Problems ◽  
Long Time ◽  
Numerical Integration Methods ◽  
Numerical Integral

Newton-Cotes integration formulae have been researched for a long time, but the topic is still of interest since the correctness of the techniques has not yet been explicitly defined in a sequence for diverse engineering situations. The purpose of this paper is to give the readers an overview of the four numerical integration methods derived from Newton-Cotes formula, namely the Trapezoidal rule, Simpson's 1/3rd rule, Simpson's 3/8th rule, and Weddle's rule, as well as to demonstrate the periodicity of the most accurate methods for solving each engineering integral equation by varying the number of sub-divisions. The exact expressions by solving the numerical integral equations have been determined by Maple program and comparisons have been done using Python version 3.8.

scholarly journals A study on numerical integration methods for rendering atmospheric scattering phenomenon

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 241-249
Author(s):  
Tomasz Gałaj ◽  
Adam Wojciechowski
Keyword(s):  
Numerical Integration ◽  
Integration Method ◽  
Single Scattering ◽  
Trapezoidal Rule ◽  
Qualitative Comparison ◽  
Integration Methods ◽  
Atmospheric Scattering ◽  
Clear Sky ◽  
Numerical Integration Methods

Abstract A qualitative comparison of three, popular and most widely known numerical integration methods in terms of atmospheric single scattering calculations is presented. A comparison of Midpoint, Trapezoidal and Simpson’s Rules taking into account quality of a clear sky generated images is performed. Methods that compute the atmospheric scattering integrals use Trapezoidal Rule. Authors try to determine which numerical integration method is the best for determining the colors of the sky and check if Trapezoidal Rule is in fact the best choice. The research does not only conduct experiments with Bruneton’s framework but also checks which of the selected numerical integration methods is the most appropriate and gives the lowest error in terms of atmospheric scattering phenomenon.

scholarly journals On the relationship between long-period comets and large trans-Neptunian planetary bodies

2016 ◽  
Vol 12 (S325) ◽  
pp. 263-265
Author(s):  
Rustam Guliyev ◽  
Ayyub Guliyev
Keyword(s):  
Solar System ◽  
Numerical Integration ◽  
Dynamical Evolution ◽  
Integration Methods ◽  
Long Period ◽  
Planetary Bodies ◽  
Numerical Integration Methods ◽  
Relationship Of ◽  
The Relationship

AbstractIn the present work we investigate the possible relationship of long-period comets with five large and distant trans-Neptunian bodies (Sedna, Eris, 2007 OR10, 2012 VP113and 2008 ST291) in order to determine the probability of the transfer of a part of these kind of comets to the inner of the Solar System. To identify such relationships, we studied the relative positions of the comet orbits and listed TNOs. Using numerical integration methods, we examined dynamical evolution of the comets and have found one encounter of comet C/1861J1 and Eris.

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