This article is cited in 5 scientific papers (total in 5 papers)
The Cauchy problem for a singularly perturbed Volterra integro-differential equation
N. N. Nefedov, A. G. Nikitin, T. A. Urazgil'dina
Faculty of Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia
The Cauchy problem for a singularly perturbed Volterra integro-differential equation is examined. Two cases are considered: (1) the reduced equation has an isolated solution, and (2) the reduced equation has intersecting solutions (the so-called case of exchange of stabilities). An asymptotic expansion of the solution to the Cauchy problem is constructed by the method of boundary functions. The results are justified by using the asymptotic method of differential inequalities, which is extended to a new class of problems.
singularly perturbed Volterra integro-differential equation, Cauchy problem, asymptotic method, differential inequalities.
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Computational Mathematics and Mathematical Physics, 2006, 46:5, 768–775
N. N. Nefedov, A. G. Nikitin, T. A. Urazgil'dina, “The Cauchy problem for a singularly perturbed Volterra integro-differential equation”, Zh. Vychisl. Mat. Mat. Fiz., 46:5 (2006), 805–812; Comput. Math. Math. Phys., 46:5 (2006), 768–775
Citation in format AMSBIB
\by N.~N.~Nefedov, A.~G.~Nikitin, T.~A.~Urazgil'dina
\paper The Cauchy problem for a~singularly perturbed Volterra integro-differential equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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