Journal ArticleDOI
A brief survey on numerical methods for solving singularly perturbed problems
Mohan K. Kadalbajoo,Vikas Gupta +1 more
TLDR
This survey paper contains a surprisingly large amount of literature on singularly perturbed problems and indeed can serve as an introduction to some of the ideas and methods for the singular perturbation problems.About:
This article is published in Applied Mathematics and Computation.The article was published on 2010-12-15. It has received 139 citations till now.read more
Citations
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Journal ArticleDOI
Robust Numerical Methods for Singularly Perturbed Differential Equations: A Survey Covering 2008–2012
TL;DR: In this article, the authors present new results in numerical analysis of singularly perturbed convection-diffusion-reaction problems that have appeared in the last five years, mainly discussing layer-adapted meshes.
A variational approach to singularly perturbed boundary value problems for ordinary and partial differential equations with turning points : (prepublication)
J. Grasman,B.J. Matkowsky +1 more
TL;DR: In this article, the authors employ a variational formulation of the singularity perturbed boundary value problem to resolve the question of the number and location of the boundary layers as well as to uniquely determine the asymptotic expansion of the solution.
Journal ArticleDOI
A review on singularly perturbed differential equations with turning points and interior layers
TL;DR: This paper reviews some existing literature on asymptotic and numerical analysis of singularly perturbed turning point and interior layer problems to find out what problems are treated and what numerical/asymptotic methods are employed, with an eye towards developing general methods to solve such problems.
Journal ArticleDOI
A finite-difference method for a singularly perturbed delay integro-differential equation
TL;DR: The purpose is to construct and analyse a numerical method with uniform convergence in the perturbation parameter for a linear first order Volterra integro-differential equation with delay using implicit difference rules for differential part and composite numerical quadrature rules for integral part.
Journal ArticleDOI
A parameter-uniform higher order finite difference scheme for singularly perturbed time-dependent parabolic problem with two small parameters
TL;DR: A parameter-uniform numerical method is constructed and analysed for solving one-dimensional singularly perturbed parabolic problems with two small parameters and is proved to be uniformly convergent of order two in both the spatial and temporal variables.
References
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Journal ArticleDOI
The Pricing of Options and Corporate Liabilities
Fischer Black,Myron S. Scholes +1 more
TL;DR: In this paper, a theoretical valuation formula for options is derived, based on the assumption that options are correctly priced in the market and it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks.
Journal ArticleDOI
A quantitative description of membrane current and its application to conduction and excitation in nerve
A. L. Hodgkin,A. F. Huxley +1 more
TL;DR: This article concludes a series of papers concerned with the flow of electric current through the surface membrane of a giant nerve fibre by putting them into mathematical form and showing that they will account for conduction and excitation in quantitative terms.
Book
Boundary layer theory
TL;DR: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part, denoted as turbulence as discussed by the authors, and the actual flow is very different from that of the Poiseuille flow.
Journal ArticleDOI
Brownian motion in a field of force and the diffusion model of chemical reactions
TL;DR: In this article, a particle which is caught in a potential hole and which, through the shuttling action of Brownian motion, can escape over a potential barrier yields a suitable model for elucidating the applicability of the transition state method for calculating the rate of chemical reactions.
Journal ArticleDOI
Impulses and Physiological States in Theoretical Models of Nerve Membrane
TL;DR: Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of non-linear differential equations with either a stable singular point or a limit cycle, which qualitatively resembles Bonhoeffer's theoretical model for the iron wire model of nerve.