Results 61 to 70 of about 12,351 (211)
A Midpoint Upwind Numerical Scheme for Singularly Perturbed Differential Difference Equations
Abstract and Applied Analysis, Volume 2026, Issue 1, 2026.In this work, we consider a class of singularly perturbed differential‐difference equations with small shift parameters in the convection and reaction terms, which frequently arise in applied mathematics and engineering. The presence of a small diffusion parameter ε, (0 < ε ≪ 1) causes the solution of the considered problem to exhibit steep gradients ...
Amare Worku Demsie +3 more
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Қарағанды университетінің хабаршысы. Математика сериясы, 2018 The article is devoted to study of boundary value problem with boundary jumps for third order linear integro-differential equation with a small parameter at the highest derivatives, provided that additional characteristic equation’s roots have opposite ...
A.E. Mirzakulova +3 more
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International Transactions on Electrical Energy Systems, Volume 2026, Issue 1, 2026.In the midst of rapid growth in the power sector, there is a pressing need to address increasing load demands and the introduction of additional electrical vehicle‐related loads. Renewable energy resources, particularly solar photovoltaics (PVs), emerge as crucial allies in meeting the rising electricity requirements. However, integrating solar PV into
Muthuveerappan S. +3 more
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A Numerical Slow Manifold Approach to Model Reduction for Optimal Control of Multiple Time Scale ODE [PDF]
, 2013 Time scale separation is a natural property of many control systems that can be ex- ploited, theoretically and numerically. We present a numerical scheme to solve optimal control problems with considerable time scale separation that is based on a model ...
Lebiedz, Dirk, Rehberg, Marcel
core
The Contrast Structures for a Class of Singularly Perturbed Systems with Heteroclinic Orbits
Discrete Dynamics in Nature and Society, 2016 Singularly perturbed problems are often used as the models of ecology and epidemiology. In this paper, a class of semilinear singularly perturbed systems with contrast structures are discussed.
Han Xu, Yinlai Jin
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Hybrid Fitted Numerical Scheme for Singularly Perturbed Spatiotemporal Delay Differential Equations
International Journal of Differential Equations, Volume 2026, Issue 1, 2026.In this study, a hybrid scheme is presented to solve a singularly perturbed time‐delay differential equation with a delay and advance term in the spatial variable. The scheme combines the midpoint upwind scheme and the cubic spline difference scheme in the outer and inner layer regions, respectively, on a nonuniform mesh for the spatial discretization,
Mulunesh Amsalu Ayele +2 more
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Parametrized Singularly Perturbed Boundary Value Problems
Journal of Mathematical Analysis and Applications, 1994 Boundary value problems for some \((\varepsilon,\lambda)\)-families of singularly perturbed higher order ordinary differential equations are considered. The author applies an approach of his paper [J. Differ. Equation 106, 312-331 (1993)] to give the lower estimates for the number of parameters \(\lambda\in \mathbb{R}^ m\) for which those equations ...
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Journal of Mathematics, Volume 2026, Issue 1, 2026.Time‐fractional fourth‐order partial differential equations (PDEs) are typically important in the modeling of complex physical systems that have long‐memory effects and high‐order transverse spatial interaction. The paper presents a new hybrid method, called the Cuckoo Search–optimized fractional physics‐informed neural network (fPINN‐CS), that, to the
Ali Alkhathlan +5 more
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Singularly perturbed elliptic problems in exterior domains
Differential and Integral Equations, 2000 The paper deals with the following problem: \[ -\varepsilon^2\Delta u+u=u^{p-1},\quad u>0\text{ in }\Omega,\quad u\in H^1_0 (\Omega) \tag{1} \] where \(\Omega\) is a domain in \(\mathbb{R}^N\) such that \(\mathbb{R}^N \setminus \Omega\) is a bounded open set ...
Dancer, E. N., Yan, Shusen
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Pattern Formation and Nonlinear Waves Close to a 1:1 Resonant Turing and Turing–Hopf Instability
Studies in Applied Mathematics, Volume 155, Issue 5, November 2025.ABSTRACT In this paper, we analyze the dynamics of a pattern‐forming system close to simultaneous Turing and Turing–Hopf instabilities, which have a 1:1 spatial resonance, that is, they have the same critical wave number. For this, we consider a system of coupled Swift–Hohenberg equations with dispersive terms and general, smooth nonlinearities.
Bastian Hilder, Christian Kuehn
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