scholarly journals Convergence Analysis of Finite Difference Method for Differential Equation

2017 ◽  
Vol 08 (03) ◽  
Author(s):  
Yizengaw N
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Convergence Analysis ◽  
Difference Method

Numerical Dynamics of Nonstandard Finite Difference Method for Nonlinear Delay Differential Equation

2018 ◽  
Vol 28 (11) ◽  
pp. 1850133 ◽  
Author(s):  
Xiaolan Zhuang ◽  
Qi Wang ◽  
Jiechang Wen
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Delay Differential Equation ◽  
Difference Method ◽  
Discrete System ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay ◽  
Nonstandard Finite Difference

In this paper, we study the dynamics of a nonlinear delay differential equation applied in a nonstandard finite difference method. By analyzing the numerical discrete system, we show that a sequence of Neimark–Sacker bifurcations occur at the equilibrium as the delay increases. Moreover, the existence of local Neimark–Sacker bifurcations is considered, and the direction and stability of periodic solutions bifurcating from the Neimark–Sacker bifurcation of the discrete model are determined by the Neimark–Sacker bifurcation theory of discrete system. Finally, some numerical simulations are adopted to illustrate the corresponding theoretical results.

Use of Finite Difference Method in the Study of Stepped Beams

1998 ◽  
Vol 26 (1) ◽  
pp. 11-24 ◽  
Author(s):  
A. Krishnan ◽  
Geetha George ◽  
P. Malathi
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Free Vibration ◽  
Difference Method ◽  
Geometric Properties ◽  
Stepped Beam

The analysis of stepped beams using finite difference method normally is carried by use of a single differential equation. Whenever the step is a node, numerical values of average geometric properties are taken for computation. It is expected that, with finer meshes, the solution will converge to an acceptable one. Free vibration studies carried out on a stepped beam do not confirm this expectation. The numerical values converge; but to wrong ones. Some details are presented in this paper.

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