A general numerical approximation of the stress characteristic field at a singular point

2019 ◽  
Author(s):  
Nor Alisa Mohd Damanhuri ◽  
Syafikah Ayob
Keyword(s):  
Singular Point ◽  
Numerical Approximation ◽  
Characteristic Field

ON THE ASYMPTOTIC EXPANSIONS OF NUMERICAL SOLUTIONS TO SECOND ORDER DIFFERENTIAL EQUATIONS WITH A REGULAR SINGULAR POINT

2001 ◽  
Vol 11 (01) ◽  
pp. 163-177
Author(s):  
RICHARD WEISS ◽  
FRANK R. de HOOG ◽  
ROBERT S. ANDERSSEN
Keyword(s):  
Differential Equation ◽  
Singular Point ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Approximation ◽  
Numerical Solutions ◽  
Second Order ◽  
Regular Singular Point ◽  
Second Order Differential Equations ◽  
Uniform Asymptotic Expansion

When difference schemes with uniformly spaced gridpoints are applied to second order ordinary differential equations with a regular singular point, it is often the case that the resulting numerical approximation does not have a uniform asymptotic expansion. As a consequence, postprocessing, such as h2-extrapolation is not an option. This paper examines the cause of this phenomenon and finds that the existence of such expansions requires the discretization of the boundary conditions at the singular point to be compatible with the discretization of the differential equation. In addition, it is shown how an understanding of the need for compatible discretization can assist in the construction of schemes for several classes of equations that arise when symmetry is used to reduce partial differential equations to ordinary differential equations with a regular singular point.

EFFECT OF CELLULAR MEMBRANE RESISTIVITY INHOMOGENEITY ON THE THERMAL NOISE-LIMIT

2015 ◽  
Vol 11 (3) ◽  
pp. 3171-3183
Author(s):  
Gyula Vincze
Keyword(s):  
Field Strength ◽  
Thermal Noise ◽  
Cellular Membrane ◽  
Thermal Limit ◽  
Low Frequencies ◽  
Membrane Resistivity ◽  
Noise Limit ◽  
The Asymmetry ◽  
Characteristic Field

Our objective is to generalize the Weaver-Astumian (WA) and Kaune (KA) models of thermal noise limit to the case ofcellular membrane resistivity asymmetry. The asymmetry of resistivity causes different effects in the two models. In the KAmodel, asymmetry decreases the characteristic field strength of the thermal limit over and increases it below the breakingfrequency (10  m), while asymmetry decreases the spectral field strength of the thermal noise limit at all frequencies.We show that asymmetry does not change the character of the models, showing the absence of thermal noise limit at highand low frequencies in WA and KA models, respectively.

First order over determined system with singular point

2007 ◽  
Vol 18 (1) ◽  
pp. 65-80
Author(s):  
Adel Nasim Adib ◽  
Nusrat Rajabov
Keyword(s):  
Singular Point ◽  
First Order

Boundary Value Problems of Electroelasticity with Concentrated Singularities

1994 ◽  
Vol 1 (5) ◽  
pp. 459-467
Author(s):  
T. Buchukuri ◽  
D. Yanakidi
Keyword(s):  
Singular Point ◽  
Boundary Value Problems ◽  
Power Function ◽  
Boundary Value ◽  
Linearly Independent

Abstract We investigate the solutions of boundary value problems of linear electroelasticity, having growth as a power function in the neighbourhood of infinity or in the neighbourhood of an isolated singular point. The number of linearly independent solutions of this type is established for homogeneous boundary value problems.

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