Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

On the solution to a class of strongly singular linear integral equations


Author: A. K. Gautesen
Journal: Quart. Appl. Math. 50 (1992), 129-140
MSC: Primary 45G05
DOI: https://doi.org/10.1090/qam/1146628
MathSciNet review: MR1146628
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A strongly singular linear integral equation containing a small positive parameter $ \delta $ is considered. This equation is transformed into a Fredholm integral equation of the second kind with a continuous kernel. The rate of convergence of the Neumann series for this integral equation is shown to be $ o\left( {{\delta ^2}} \right)$. An example from fracture mechanics is considered in detail.


References [Enhancements On Off] (What's this?)

  • [1] A. K. Gautesen, On the asymptotic solution to a class of linear integral equations, SIAM J. Appl. Math. 48, 294-306 (1988) MR 933036
  • [2] M. Hori and S. Nemat-Nasser, Asymptotic solution to a class of strongly singular integral equations, SIAM J. Appl. Math. 50, 716-725 (1990) MR 1050909
  • [3] S. Nemat-Nasser and M. Hori, Toughening by partial or full bridging of cracks in ceramics and fiber reinforced composites, Mechics of Materials 6, 245-269 (1987)
  • [4] W. E. Olmstead and A. K. Gautesen, Asymptotic solution of some singularly perturbed Fredholm integral equations, Z. Angew. Math. Phys. 40, 230-244 (1989) MR 990629
  • [5] J. R. Willis and S. Nemat-Nasser, Singular perturbation solution of a class of singular integral equations, Quart. Appl. Math. 48, 741-753 (1990) MR 1079917

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 45G05

Retrieve articles in all journals with MSC: 45G05


Additional Information

DOI: https://doi.org/10.1090/qam/1146628
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society