Computational Method for Singularly Perturbed Parabolic Differential Equations with Discontinuous Coefficients and Large Delay

2021 ◽  
Author(s):  
Imiru Takele Daba ◽  
Gemechis File Duressa
Keyword(s):  
Differential Equations ◽  
Discontinuous Coefficients ◽  
Computational Method ◽  
Singularly Perturbed ◽  
Parabolic Differential Equations ◽  
Large Delay

Singularly perturbed differential equations with discontinuous coefficients and concentrated factors

2004 ◽  
Vol 158 (3) ◽  
pp. 683-701 ◽  
Author(s):  
Ivanka Tr. Angelova ◽  
Lubin G. Vulkov
Keyword(s):  
Differential Equations ◽  
Discontinuous Coefficients ◽  
Singularly Perturbed

scholarly journals Computational method for singularly perturbed delay differential equations with twin layers or oscillatory behaviour

2015 ◽  
Vol 6 (1) ◽  
pp. 391-398 ◽  
Author(s):  
D. Kumara Swamy ◽  
K. Phaneendra ◽  
A. Benerji Babu ◽  
Y.N. Reddy
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Computational Method ◽  
Singularly Perturbed ◽  
Oscillatory Behaviour ◽  
Delay Differential

scholarly journals Robust numerical method for singularly perturbed differential equations having both large and small delay

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Habtamu Garoma Debela
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Uniform Mesh ◽  
Large Delay ◽  
Content Type ◽  
Small Delay ◽  
Numerical Experimentation ◽  
The Stability

PurposeThe purpose of this study is to develop stable, convergent and accurate numerical method for solving singularly perturbed differential equations having both small and large delay.Design/methodology/approachThis study introduces a fitted nonpolynomial spline method for singularly perturbed differential equations having both small and large delay. The numerical scheme is developed on uniform mesh using fitted operator in the given differential equation.FindingsThe stability of the developed numerical method is established and its uniform convergence is proved. To validate the applicability of the method, one model problem is considered for numerical experimentation for different values of the perturbation parameter and mesh points.Originality/valueIn this paper, the authors consider a new governing problem having both small delay on convection term and large delay. As far as the researchers' knowledge is considered numerical solution of singularly perturbed boundary value problem containing both small delay and large delay is first being considered.

scholarly journals Robust numerical method for singularly perturbed parabolic differential equations with negative shifts

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2383-2401
Author(s):  
Mesfin Woldaregay ◽  
Gemechis Duressa
Keyword(s):  
Differential Equations ◽  
Mesh Size ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Spatial Discretization ◽  
Parabolic Differential Equations ◽  
First Order ◽  
Temporal Discretization ◽  
Solution Bound ◽  
The Stability

This paper deals with numerical treatment of singularly perturbed parabolic differential equations having delay on the zeroth and first order derivative terms. The solution of the considered problem exhibits boundary layer behaviour as the perturbation parameter tends to zero. The equation is solved using ?-method in temporal discretization and exponentially fitted finite difference method in spatial discretization. The stability of the scheme is proved by using solution bound technique by constructing barrier functions. The parameter uniform convergence analysis of the scheme is carried out and it is shown to be accurate of order O(N-2/N-1+c?+(?t)2) for the case ?= 1/2, where N is the number of mesh points in spatial discretization and ?t is the mesh size in temporal discretization. Numerical examples are considered for validating the theoretical analysis of the scheme.

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