Ramm, A. G.; Shifrin, E. I. Asymptotics of the solution to a singularly perturbed integral equation. (English) Zbl 0718.45006 Appl. Math. Lett. 4, No. 1, 67-70 (1991). Summary: The leading term of the asymptotics as \(\epsilon \to +0\) of the solution to the equation \(\epsilon h_{\epsilon}+\int^{1}_{-1}\exp (-a| x-y|)h_{\epsilon}(y)dy=f(x),\) \(-1\leq x\leq 1,\) \(f\in C^ 4(-1,1)\) is calculated. Cited in 1 Document MSC: 45M05 Asymptotics of solutions to integral equations 45B05 Fredholm integral equations Keywords:asymptotics; singular perturbation; leading term PDF BibTeX XML Cite \textit{A. G. Ramm} and \textit{E. I. Shifrin}, Appl. Math. Lett. 4, No. 1, 67--70 (1991; Zbl 0718.45006) Full Text: DOI References: [1] Ramm, A.G., Numerical solution of integral equations in a space of distributions, J. math. anal. appl., 110, 384-390, (1985) · Zbl 0627.65141 [2] Ramm, A.G., Random fields estimation theory, (1990), Longman Scientific and Wiley New York · Zbl 0712.47042 [3] Ramm, A.G., Theory and applications of some new classes of integral equations, (1980), Springer-Verlag New York · Zbl 0456.45001 [4] A.G. Ramm, Numerical solution of some integral equations in distributions, Computers and Math. with Applications (to appear). · Zbl 0627.65141 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.