scholarly journals Object-Oriented Implementation of Software for Solving Ordinary Differential Equations

1993 ◽  
Vol 2 (4) ◽  
pp. 217-225 ◽  
Author(s):  
Kjell Gustafsson
Keyword(s):  
User Interface ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Integration ◽  
Integration Method ◽  
Object Oriented ◽  
Software Components ◽  
Integration Methods ◽  
Numerical Integration Methods

We describe an object-oriented implementation of numerical integration methods for solving ordinary differential equations. Software components that are common to many different integration methods have been identified and implemented in such a way that they can be reused. This facilitates the design of a uniform user interface and makes the task of implementing a new integration method fairly modest. The sharing of code in this type of implementation also allows for less subjective comparisons of the result from different integration methods.

scholarly journals Comparative Study of the Advantages of Structural Numerical Integration Methods for Ordinary Differential Equations

2017 ◽  
Vol 4 (53) ◽  
pp. 51 ◽  
Author(s):  
Vladimir Petrovish Bubnov ◽  
Alexey Sergeevich Eremin ◽  
Nikolai Aleksandrovich Kovrizhnykh ◽  
Igor Vladimirovich Olemskoy
Keyword(s):  
Differential Equations ◽  
Comparative Study ◽  
Ordinary Differential Equations ◽  
Numerical Integration ◽  
Integration Methods ◽  
Numerical Integration Methods

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.

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