The P-stability of backward differentiation method for singularly perturbed Volterra integral equations with delay argument

2004 ◽  
Vol 154 (3) ◽  
pp. 881-887
Author(s):  
Modi H. Alnasr
Keyword(s):  
Integral Equations ◽  
Volterra Integral Equations ◽  
Singularly Perturbed ◽  
Delay Argument ◽  
Differentiation Method ◽  
Equations With Delay

Singularly Perturbed Volterra Integral Equations II

1987 ◽  
Vol 47 (6) ◽  
pp. 1150-1162 ◽  
Author(s):  
J. S. Angell ◽  
W. E. Olmstead
Keyword(s):  
Integral Equations ◽  
Volterra Integral Equations ◽  
Singularly Perturbed

scholarly journals Singularly perturbed Volterra integral equations with weakly singular kernels

2002 ◽  
Vol 30 (3) ◽  
pp. 129-143 ◽  
Author(s):  
Angelina Bijura
Keyword(s):  
Integral Equations ◽  
Special Function ◽  
Initial Boundary ◽  
Volterra Integral Equations ◽  
Singularly Perturbed ◽  
Interesting Aspect ◽  
Weakly Singular Kernels ◽  
Weakly Singular ◽  
Singular Kernels ◽  
Linear Volterra Integral Equations

We consider finding asymptotic solutions of the singularly perturbed linear Volterra integral equations with weakly singular kernels. An interesting aspect of these problems is that the discontinuity of the kernel causes layer solutions to decay algebraically rather than exponentially within the initial (boundary) layer. To analyse this phenomenon, the paper demonstrates the similarity that these solutions have to a special function called the Mittag-Leffler function.

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