Midpoint methods for a Volterra integral equation with non-smooth solutions

2012 ◽  
Vol 1 (2) ◽  
Author(s):  
Ali Salimi shamloo ◽  
Mahtab Aliakbar Naeim
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation ◽  
Smooth Solutions

scholarly journals Numerical methods for a Volterra integral equation with non-smooth solutions

2006 ◽  
Vol 189 (1-2) ◽  
pp. 412-423 ◽  
Author(s):  
Teresa Diogo ◽  
Neville J. Ford ◽  
Pedro Lima ◽  
Svilen Valtchev
Keyword(s):  
Integral Equation ◽  
Numerical Methods ◽  
Volterra Integral Equation ◽  
Smooth Solutions

THE RESOLUTION CORRECTION IN THE SCINTILLATION SPECTROMETRY OF CONTINUOUS X RAYS

1958 ◽  
Vol 36 (12) ◽  
pp. 1624-1633 ◽  
Author(s):  
W. R. Dixon ◽  
J. H. Aitken
Keyword(s):  
Integral Equation ◽  
Numerical Analysis ◽  
Numerical Methods ◽  
Analytical Procedure ◽  
Pulse Height ◽  
Matrix Inversion ◽  
Height Distribution ◽  
X Rays ◽  
Smooth Solutions ◽  
Pulse Height Distribution

The problem of making resolution corrections in the scintillation spectrometry of continuous X rays is discussed. Analytical solutions are given to the integral equation which describes the effect of the statistical spread in pulse height. The practical necessity of making some kind of numerical analysis is pointed out. Difficulties with numerical methods arise from the fact that the observed pulse-height distribution cannot be defined precisely. As a result it is possible in practice only to find smooth "solutions". Additional difficulties arise if the numerical method is based on an invalid analytical procedure. For example matrix inversion is of doubtful value in making the resolution correction because there does not appear to be an inverse kernel for the integral equation in question.

On the Volterra integral equation relating creep and relaxation

2008 ◽  
Vol 24 (3) ◽  
pp. 035009 ◽  
Author(s):  
R S Anderssen ◽  
A R Davies ◽  
F R de Hoog
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation
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