A uniform numerical method for dealing with a singularly perturbed delay initial value problem

Amiraliyeva, I. G.; Erdoğan, Fevzi; Amiraliyev, Gabil M.

doi:10.1016/j.aml.2010.06.002

Cited by 48 publications

(18 citation statements)

References 11 publications

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“…In [104], consider an initial value problem (IVP) for the nonlinear second-order singularly perturbed delay I to be specified, A is a constant and r is a constant delay, which is independent of .…”

Section: Delay Differential Equationsmentioning

confidence: 99%

Various Numerical Methods for Singularly Perturbed Boundary Value Problems

Mishra¹,

Saini²

2014

AJAMS

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The numerical treatment of singular perturbation problems is currently a field in which active research is going on these days. Singular perturbation problems in which the term containing the highest order derivative is multiplied by a small parameter ε , occur in a number of areas of applied mathematics, science and engineering among them fluid mechanics (boundary layer problems) elasticity (edge effort in shells) and quantum mechanics. In this paper, we consider few numerical methods for singularly perturbed boundary value problems developed by numerous researchers between 2006 to 2013. A Summary of the result of some recent methods is presented and this leads to conclusion and recommendations regarding methods to use on singular perturbation problem.

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Section: Delay Differential Equationsmentioning

confidence: 99%

Various Numerical Methods for Singularly Perturbed Boundary Value Problems

Mishra¹,

Saini²

2014

AJAMS

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“…"It faetures regieons called "boundary layers"" where the breachmodify fast" . And these equations as well as numericale methodes have been learned by a number of author [16][17][18][19][20]. "In this paper, produce modern Method to Approximate Solution of the singularly perturbed problems with boundary condition on Chebyshev polynomial" .…”

Section: Introductionmentioning

confidence: 99%

Chebyshev Polynomials in Collocation Methods for Solving Singular Perturbation Problems

2018

QJPS

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This paper discourse the utility Momentmethod on second, third and fourth kind Chebyshev polynomials as attempt functions in solution singular perturbation problems with boundary condition" . "The process is computational very unmingled and magnetic" . "Applications are justly demonstrated through numerical examples to illustrated the effectiveness and easiness of the approximate, all the calculation outcome are obtain using Matlab" .

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“…Amiraliyev and Erdoğan [8] studied uniform method for singularly perturbed delay differential equations. Amiraliyeva, Erdoğan and Amiraliyev [9] applied a uniform numerical method for dealing with a singularly perturbed delay initial value problem. Adzic and Ovcin [10] studied nonlinear spp with nonlocal boundary conditions and spectral approximation.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Method for Nonlinear Singularly Perturbed Multi-Point Boundary Value Problem

Cakir¹,

Arslan²

2016

JAMP

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We consider a uniform finite difference method for nonlinear singularly perturbed multi-point boundary value problem on Shishkin mesh. The problem is discretized using integral identities, interpolating quadrature rules, exponential basis functions and remainder terms in integral form. We show that this method is the first order convergent in the discrete maximum norm for original problem (independent of the perturbation parameter ε). To illustrate the theoretical results, we solve test problem and we also give the error distributions in the solution in Table 1 and Figures 1-3.

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A uniform numerical method for dealing with a singularly perturbed delay initial value problem

Cited by 48 publications

References 11 publications

Various Numerical Methods for Singularly Perturbed Boundary Value Problems

Various Numerical Methods for Singularly Perturbed Boundary Value Problems

Chebyshev Polynomials in Collocation Methods for Solving Singular Perturbation Problems

A Numerical Method for Nonlinear Singularly Perturbed Multi-Point Boundary Value Problem

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