An analysis of the finite-difference method for one-dimensional Klein–Gordon equation on unbounded domain

2009 ◽  
Vol 59 (7) ◽  
pp. 1568-1583 ◽  
Author(s):  
Houde Han ◽  
Zhiwen Zhang
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Unbounded Domain ◽  
Difference Method ◽  
Gordon Equation ◽  
One Dimensional ◽  
Klein Gordon ◽  
The Finite Difference Method ◽  
Klein Gordon Equation

Finite-Difference Modelling for a One-Dimensional Rectangular Estuary

1992 ◽  
Vol 26 (9-11) ◽  
pp. 2591-2594
Author(s):  
Y. S. Sin
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Tidal Cycle ◽  
Open Boundary ◽  
One Dimensional ◽  
Step Procedure ◽  
Tidal Velocity ◽  
The Finite Difference Method ◽  
Analysis Of Dispersion

A numerical method for the analysis of dispersion of pollutants in a one-dimensional rectangular estuary within a tidal cycle is presented. The finite-difference method is used to obtain a solution for the partial differential equation. An explicit scheme using multi-step procedure is adopted for solving the problem. It is shown that an analytical method is capable of predicting the dispersion of a slug load in the estuary as long as the effect due to the open boundary is negligible. However, the finite-difference method is required to study the dispersion effect of a continuous or variable pollutant source subjected to variable tidal velocity. The model developed is also applied in determining the effect of salinity intrusion within a tidal cycle due to different fresh water flows.

Transients During a Railway Air Brake Release Demand

1990 ◽  
Vol 204 (1) ◽  
pp. 31-38 ◽  
Author(s):  
M A Murtaza ◽  
S B L Garg
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Difference Method ◽  
Laboratory Data ◽  
One Dimensional ◽  
The Finite Difference Method ◽  
Air Brake System ◽  
Good Agreement

This paper deals with the simulation of railway air brake release demand of a twin-pipe graduated release railway air brake system based on the solution of partial differential equations governing one-dimensional flow by the finite difference method supported by extrapolation/interpolation. Air brake release demand is simulated as an exponential input of pressure. The analysis incorporates the corrections needed to be used for various restrictions in the brake pipeline. Results are in good agreement with the laboratory data.

APPLICATION OF A NUMERICAL-ANALYTICAL METHOD FOR SOLVING A ONE-DIMENSIONAL WAVE EQUATION

Akustika ◽  
2021 ◽  
pp. 22
Author(s):  
Vladimir Mondrus ◽  
Dmitrii Sizov
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Analytical Method ◽  
One Dimensional ◽  
Numerical Analytical Method ◽  
The Finite Difference Method ◽  
Dimensional Wave

The article contains a solution to the problem of wave propagation in a one-dimensional rod from the initial impact. A numerical-analytical method is used to solve the problem. The numerical part of the method is based on the application of the idea of the finite difference method. The analytical part uses the concept of Green’s function to solve the problem in terms of the spatial coordinate in the considered area. The results include graphs of the solution obtained at different points in time.

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