A. V. Zaborskiy, A. V. Nesterov, “The asymptotic decomposition of solution of singularly perturbed differential and operational nonlinear equation with variable coefficients”, Mat. Model., 2016, Volume 28, Number 1,Pages <nobr>117

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The asymptotic decomposition of solution of singularly perturbed differential and operational nonlinear equation with variable coefficients

A. V. Zaborskiy^ab, A. V. Nesterov^ab

^a Obninsk Institute for Nuclear Power Engineering – Branch of Federal State Higher Education «National Research Nuclear University MEPhI»
^b Moscow City Pedagogical University

Abstract: Formal asymptotic decomposition on small parameter of solution for initial task for singularly perturbed differential and operator nonlinear equation with variable coefficients in critical case is constructed. Estimates of functions of splash and boundary functions are found, assessment of residual member of decomposition is received.

Keywords: asymptotic decomposition of solution, small parameter, singularly perturbations, differential and operator equations, initial task, critical case, modified method of boundary functions.

UDC: 517.953

Received: 18.11.2014