A Two-parameter Family of Two-level Higher Order Difference Methods for the Two-dimensional Heat Equation

1975 ◽  
Vol 16 (2) ◽  
pp. 193-205 ◽  
Author(s):  
H. M. KHALIL ◽  
J. H. GIESE
Keyword(s):  
Heat Equation ◽  
Higher Order ◽  
Parameter Family ◽  
Two Dimensional ◽  
Order Difference ◽  
Difference Methods ◽  
Two Parameter

Weir flows and waterfalls

1991 ◽  
Vol 230 ◽  
pp. 525-539 ◽  
Author(s):  
Frédéric Dias ◽  
E. O. Tuck
Keyword(s):  
Vertical Wall ◽  
Finite Depth ◽  
Free Surface Flows ◽  
Parameter Family ◽  
The Other ◽  
Two Dimensional ◽  
Surface Flows ◽  
Supercritical Solutions ◽  
Subcritical Solutions ◽  
Two Parameter

Two-dimensional free-surface flows, which are uniform far upstream in a channel of finite depth that ends suddenly, are computed numerically. The ending is in the form of a vertical wall, which may force the flow upward before it falls down forever as a jet under the effect of gravity. Both subcritical and supercritical solutions are presented. The subcritical solutions are a one-parameter family of solutions, the single parameter being the ratio between the height of the wall and the height of the uniform flow far upstream. On the other hand, the supercritical solutions are a two-parameter family of solutions, the second parameter being the Froude number. Moreover, for some combinations of the parameters, it is shown that the solution is not unique.

scholarly journals A Comparison of Higher-Order Difference Methods in the Solution of Beam-Vibration Problems

SIMULATION ◽  
1964 ◽  
Vol 3 (1) ◽  
pp. 33-44 ◽  
Author(s):  
Donald T. Greenwood
Keyword(s):  
Boundary Conditions ◽  
Analog Computer ◽  
Higher Order ◽  
Difference Approximation ◽  
Frequency Error ◽  
Central Difference ◽  
Final Choice ◽  
Order Difference ◽  
Difference Methods ◽  
Passive Circuit

Several higher-order difference methods are investi gated and compared for the problem of finding the natural frequencies of the lateral vibration of a beam. All of the methods considered are applicable to either digital or analog computers, although particu lar reference is made to the analog computer. The methods considered in most detail use the same basic central difference approximation, the variations occurring in the method of representing boundary conditions. Three higher-order approaches to the problem of boundary conditions are pre sented. They are 1) the use of one-sided differences of fourth order, 2) the use of symmetry assumptions, and 3) the passive-circuit approach. Each method is shown to have its advantages, the final choice de pending upon the particular requirements of the problem. Results are presented in the form of curves of per centage mode-frequency error vs number of cells for the various approximation methods.

scholarly journals Persistent two-dimensional strange attractors for a two-parameter family of Expanding Baker Maps

2019 ◽  
Vol 24 (2) ◽  
pp. 657-670 ◽  
Author(s):  
Antonio Pumariño ◽  
◽  
José Ángel Rodríguez ◽  
Enrique Vigil
Keyword(s):  
Parameter Family ◽  
Strange Attractors ◽  
Two Dimensional ◽  
Two Parameter
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