Singularly perturbed problems in partial differential equations: A survey

DOI10.1016/S0096-3003(01)00291-0zbMath1024.35007OpenAlexW2083512511MaRDI QIDQ1855941

Mohan K. Kadalbajoo, Kailash C. Patidar

Publication date: 28 January 2003

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0096-3003(01)00291-0

zbMATH Keywords

asymptotic analysisboundary layer

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02)

Related Items (35)

Traveling wave solutions and stability behaviours under advection dominance for singularly perturbed advection-diffusion-reaction processes ⋮ High order parameter uniform numerical method for singular perturbation problems ⋮ A rational spectral collocation method for third-order singularly perturbed problems ⋮ A robust numerical scheme for singularly perturbed parabolic reaction-diffusion problems via the method of lines ⋮ Robust numerical method for singularly perturbed semilinear parabolic differential difference equations ⋮ Singular perturbation results for linear partial differential-algebraic equations of hyperbolic type ⋮ Stability analysis of coupled linear ODE-hyperbolic PDE systems with two time scales ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ Parameter robust higher‐order finite difference method for convection‐diffusion problem with time delay ⋮ A robust higher-order finite difference technique for a time-fractional singularly perturbed problem ⋮ Tikhonov theorem for linear hyperbolic systems ⋮ A uniformly convergent numerical algorithm on harmonic \((H(\ell))\) mesh for parabolic singularly perturbed convection-diffusion problems with boundary layer ⋮ Uniformly convergent finite difference methods for singularly perturbed parabolic partial differential equations with mixed shifts ⋮ On the monotonicity of limit wave speed of the pgKdV equation with nonlinear terms of arbitrary higher degree ⋮ An optimal asymptotic-numerical method for convection dominated systems having exponential boundary layers ⋮ On the summability of formal solutions for doubly singular nonlinear partial differential equations ⋮ A robust uniformly convergent finite difference scheme for the time-fractional singularly perturbed convection-diffusion problem ⋮ A uniformly convergent finite difference scheme for Robin type singularly perturbed parabolic convection diffusion problem ⋮ A review on singularly perturbed differential equations with turning points and interior layers ⋮ Stochastic perturbations of periodic orbits with sliding ⋮ On singularly perturbed partial integro-differential equations with irregular singularity ⋮ Experiments with a local adaptive grid \(h\)-refinement for the finite-difference solution of BVPs in singularly perturbed second-order ODEs ⋮ A robust fitted operator finite difference method for singularly perturbed problems whose solution has an interior layer ⋮ Unnamed Item ⋮ A singularly perturbed differential equation with piecewise constant argument of generalized type ⋮ \(\varepsilon\)-uniformly convergent fitted mesh finite difference methods for general singular perturbation problems ⋮ Singular perturbation approximation by means of a \(H^2\) Lyapunov function for linear hyperbolic systems ⋮ A robust fitted numerical method for singularly perturbed turning point problems whose solution exhibits an interior layer ⋮ An efficient numerical method for coupled systems of singularly perturbed parabolic delay problems ⋮ Computation and asymptotic analysis in the impact problem ⋮ A new way to generate an exponential finite difference scheme for 2D convection-diffusion equations ⋮ Error control for approximate solutions of a class of singularly perturbed boundary value problems ⋮ Singular perturbation margin and generalised gain margin for linear time-invariant systems ⋮ A high order convergent adaptive numerical method for singularly perturbed nonlinear systems ⋮ High order fitted operator numerical method for self-adjoint singular perturbation problems

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