Robust numerical method for singularly perturbed differential equations having both large and small delay [PDF]
Arab Journal of Mathematical Sciences, 2022 Purpose – The purpose of this study is to develop stable, convergent and accurate numerical method for solving singularly perturbed differential equations having both small and large delay.
Habtamu Garoma Debela
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The Cauchy problem for singularly perturbed higher-order integro-differential equations
Вестник КазНУ. Серия математика, механика, информатика, 2019 The article is devoted to research the Cauchy problem for singularly perturbed higher-order linear integro-differential equation with a small parameter at the highest derivatives, provided that the roots of additional characteristic equation have ...
A. E. Mirzakulova +3 more
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A singularly perturbed semilinear reaction-diffusion problem in a polygonal domain [PDF]
, 2010 The semilinear reaction-di®usion equation ¡"24u+b(x; u) = 0 with Dirichlet bound-ary conditions is considered in a convex polygonal domain. The singular perturbation parameter ε is arbitrarily small, and the “reduced equation” b(x, u0 (x)) = 0 may have ...
Kellogg, R. Bruce, Kopteva, Natalia
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Alexandria Engineering Journal, 2023 The dynamical properties of a class of difference equations with continuous arguments of the form x(t)=g(x(t-r1),x(t-r2)) and its singularly perturbed counterpart ∊dxdt=-x(t)+g(x(t-r1),x(t-r2)) are investigated here.
A.M.A. EL-Sayed +2 more
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The linear quadratic regulator problem for a class of controlled systems modeled by singularly perturbed Ito differential equations [PDF]
, 2012 Link to a related website: https://digital.library.adelaide.edu.au/dspace/bitstream/2440/77907/1/hdl_77907.pdf, Open Access via UnpaywallThis paper discusses an infinite-horizon linear quadratic (LQ) optimal control problem involving state- and control ...
Shi, Peng +5 more
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Higher order energy expansions for some singularly perturbed Neumann problems [PDF]
, 2003 We consider the following singularly perturbed semilinear elliptic problem: \epsilon^{2} \Delta u - u + u^p=0 \ \ \mbox{in} \ \Omega, \quad u>0 \ \ \mbox{in} \ \ \Omega \quad \mbox{and} \ \frac{\partial u}{\partial \nu} =0 \ \mbox{on} \ \partial \
Winter, M +5 more
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Symmetry of Nodal Solutions for Singularly Perturbed Elliptic Problems on a Ball [PDF]
, 2004 In [40], it was shown that the following singularly perturbed Dirichlet problem \ep^2 \Delta u - u+ |u|^{p-1} u=0, \ \mbox{in} \ \Om,\] \[ u=0 \ \mbox{on} \ \partial \Om has a nodal solution u_\ep which has the least energy among all nodal solutions.
Winter, M +5 more
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Multiple boundary peak solutions for some singularly perturbed Neumann problems [PDF]
, 2000 We consider the problem \left \{ \begin{array}{rcl} \varepsilon^2 \Delta u - u + f(u) = 0 & \mbox{ in }& \ \Omega\\ u > 0 \ \mbox{ in} \ \Omega, \ \frac{\partial u}{\partial \nu} = 0 & \mbox{ on }& \ \partial\Omega, \end{array} \right. where \
Gui, Changfeng +8 more
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Singularly Perturbed Problems: Asymptotic Analysis and Approximate Solution
, 2022 This book collects papers from the Special Issue "Singularly Perturbed Problems: Asymptotic Analysis and Approximate Solution", published in Axioms. These papers cover different aspects of singular perturbation theory and its applications: axiomatic ...
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Exponential stability for singularly perturbed systems with state delays
Electronic Journal of Qualitative Theory of Differential Equations, 2000 In this paper the problem of stability of the zero solution of singularly perturbed system of linear differential equation with state delays is investigated.
V. Dragan, A. Ionita
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