Parameter‐robust higher‐order time‐accurate computational method for singularly perturbed time‐dependent semilinear convection‐diffusion PDEs with discontinuous data
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DOI: 10.1002/mma.10070
Abstract: This article is concerned with a class of singularly perturbed semilinear parabolic convection‐diffusion partial differential equations (PDEs) with discontinuous source function. Solutions of these PDEs usually exhibit a weak interior layer at one side of… read more here.
Keywords: singularly perturbed; method; time; solution ... See more keywords
A computational approach for 2D elliptic singularly perturbed weakly coupled systems of convection–diffusion type with multiple scales and parameters in the diffusion and the convection terms
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DOI: 10.1002/mma.10204
Abstract: In this work, we consider the efficient resolution of a 2D elliptic singularly perturbed weakly coupled system of convection–diffusion type, which has small parameters at both the diffusion and the convection terms. We assume that… read more here.
Keywords: singularly perturbed; perturbed weakly; weakly coupled; elliptic singularly ... See more keywords
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
A Study on Time‐Dependent Two Parameter Singularly Perturbed Problems via Trigonometric Quintic B‐Splines on an Exponentially Graded Mesh
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DOI: 10.1002/nme.70146
Abstract: This paper presents a fresh perspective on solving two‐parameter singularly perturbed parabolic convection‐diffusion‐reaction equations with Dirichlet boundary conditions. The methodology integrates the Crank–Nicolson (CN) scheme for discretizing temporal derivatives and applies the Trigonometric Quintic B‐splines… read more here.
Keywords: two parameter; singularly perturbed; parameter; parameter singularly ... 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