On existence of kink and antikink wave solutions of singularly perturbed Gardner equation
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DOI: 10.1002/mma.6204
Abstract: In this paper, we study the existence of kink and antikink wave solutions of singularly perturbed Gardner equation from the geometric perspective. We obtain the sufficient conditions to guarantee the existence of kink and antikink… read more here.
Keywords: solutions singularly; wave solutions; antikink wave; existence kink ... See more keywords
Some remarks on the renormalization group and Chapman‐Enskog type methods in singularly perturbed problems
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DOI: 10.1002/mma.6273
Abstract: In this paper, we show that for a large class of singularly perturbed problems, the classical Chapman‐Enskog asymptotic procedure leads, in a shorter way, to the same asymptotic expansion as the renormalization group (RG) approach.… read more here.
Keywords: perturbed problems; singularly perturbed; chapman enskog; renormalization group ... See more keywords
An Iterative Tikhonov Regularization for Solving Singularly Perturbed Elliptic PDE
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DOI: 10.1007/s00009-017-0980-0
Abstract: In this paper, we consider a class of singularly perturbed elliptical problems with homogeneous boundary conditions. We consider a regularized iterative method for solving such problems. Convergence analysis and error estimate are derived. The regularization… read more here.
Keywords: singularly perturbed; iterative tikhonov; regularization solving; solving singularly ... See more keywords
An Improved Extrapolated Collocation Technique for Singularly Perturbed Problems using Cubic B-Spline Functions
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DOI: 10.1007/s00009-021-01738-0
Abstract: In this paper, an improved extrapolated collocation method with cubic B-spline as basis functions is presented. This method is applied to a class of self-adjoint singularly perturbed boundary value problems, with the equispaced discretization of… read more here.
Keywords: cubic spline; extrapolated collocation; singularly perturbed; collocation ... See more keywords
Multiple interior and boundary peak solutions to singularly perturbed nonlinear Neumann problems under the Berestycki–Lions condition
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DOI: 10.1007/s00208-016-1412-3
Abstract: Let $$\varOmega $$Ω be a smooth bounded domain in $$\mathbb {R}^N$$RN, $$N\ge 3$$N≥3. We consider the following singularly perturbed nonlinear elliptic problem on $$\varOmega $$Ω, $$\begin{aligned} \varepsilon ^2\varDelta v-v+f(v)=0,\quad v>0\ \text {on}\ \varOmega ,\qquad \frac{\partial… read more here.
Keywords: multiple interior; singularly perturbed; berestycki lions; perturbed nonlinear ... See more keywords
Transparent boundary conditions and numerical computation for singularly perturbed telegraph equation on unbounded domain
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DOI: 10.1007/s00211-020-01115-1
Abstract: In this paper, we study the numerical solution for the singularly perturbed telegraph equation (SPTE) on unbounded domain. Firstly, we investigate the first consistent effective asymptotic expansion for the solution of SPTE by the asymptotic… read more here.
Keywords: singularly perturbed; boundary conditions; telegraph equation; perturbed telegraph ... See more keywords
A new numerical method for singularly perturbed turning point problems with two boundary layers based on reproducing kernel method
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DOI: 10.1007/s10092-016-0196-x
Abstract: In this paper, a simple numerical method is proposed for solving singularly perturbed boundary layers problems exhibiting twin boundary layers. The method avoids the choice of fitted meshes. Firstly the original problem is transformed into… read more here.
Keywords: numerical method; singularly perturbed; reproducing kernel; boundary layers ... See more keywords
Analysis of the SDFEM for singularly perturbed differential–difference equations
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DOI: 10.1007/s10092-018-0265-4
Abstract: In this paper, the stability and accuracy of a streamline diffusion finite element method (SDFEM) for the singularly perturbed differential–difference equation of convection term with a small shift is considered. With a special choice of… read more here.
Keywords: singularly perturbed; differential difference; perturbed differential; sdfem singularly ... See more keywords
An Efficient DWR-Type a Posteriori Error Bound of SDFEM for Singularly Perturbed Convection–Diffusion PDEs
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DOI: 10.1007/s10915-021-01749-9
Abstract: This article deals with the residual-based a posteriori error estimation in the standard energy norm for the streamline-diffusion finite element method (SDFEM) for singularly perturbed convection–diffusion equations. The well-known dual-weighted residual (DWR) technique has been… read more here.
Keywords: error bound; posteriori error; sdfem singularly; diffusion ... See more keywords
On Numerical Solution of Singularly Perturbed Optimal Control Problems
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DOI: 10.1007/s10957-017-1138-8
Abstract: We study singularly perturbed optimal control problems in which optimal controls may take the form of rapidly oscillating functions. Such rapidly oscillating controls can be constructed on the basis of solutions of certain approximating averaged… read more here.
Keywords: singularly perturbed; numerical solution; control problems; perturbed optimal ... See more keywords
Coordination of networked delayed singularly perturbed systems with antagonistic interactions and switching topologies
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DOI: 10.1007/s11071-017-3483-4
Abstract: This paper studies the bipartite consensus issue of networked delayed singularly perturbed systems with antagonistic interactions and switching topologies. Each singularly perturbed system contains both fast and slow dynamics as well as time-varying delay, which… read more here.
Keywords: singularly perturbed; perturbed systems; antagonistic interactions; delayed singularly ... See more keywords