Numerical Solution of Stiff Equations

2005 ◽  
pp. 619-647
Keyword(s):  
Numerical Solution ◽  
Stiff Equations

scholarly journals Three-Step Two-Hybrid Block Method for the Direct Solution of Second-Order Ordinary Differential Equations

2020 ◽  
pp. 15-23
Author(s):  
Raymond Dominic ◽  
Kyagya Yusuf T.
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Basic Function ◽  
Second Order ◽  
Direct Solution ◽  
Block Method ◽  
Stiff Equations ◽  
Two Hybrid

In this paper a three-step two hybrid block method with two offgrid hybrid points chosen within interval [Xn,Xn+1] and [Xn+1,Xn+2] was developed to solve second Order Ordinary Differential Equations directly, using the power series as the basic function to approximate and generate some continuous schemes. The basic properties of the method was investigated and was found to converge. Numerical Solution of our method was tested on some stiff equations and was found to give better approximation than the existing method.

Backscattering Analysis of Cylinder Shaped Scatterer in Vegetation Medium: Comparison Between Theories

2020 ◽  
Vol 2 (1) ◽  
pp. 15-18
Author(s):  
Syabeela Syahali ◽  
Ewe Hong Tat ◽  
Gobi Vetharatnam ◽  
Li-Jun Jiang ◽  
Hamsalekha A Kumaresan
Keyword(s):  
Numerical Solution ◽  
Cross Section ◽  
Traditional Method ◽  
Microwave Remote Sensing ◽  
Solution Model ◽  
Complex Nature ◽  
Good Match ◽  
Equivalent Source ◽  
Backscattering Cross Section ◽  
Method Model

This paper analyses the backscattering cross section of a cylinder both using traditional method model and a new numerical solution model, namely Relaxed Hierarchical Equivalent Source Algorithm (RHESA). The purpose of this study is to investigate the prospect of incorporating numerical solution model into volume scattering calculation, to be applied into microwave remote sensing in vegetation area. Results show a good match, suggesting that RHESA may be suitable to be used to model the more complex nature of vegetation medium.

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