Fitted Finite Difference Method for Third Order Singularly Perturbed Delay Differential Equations of Convection Diffusion Type

2019 ◽  
Vol 16 (05) ◽  
pp. 1840007 ◽  
Author(s):  
R. Mahendran ◽  
V. Subburayan
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Difference Method ◽  
Delay Differential Equations ◽  
Singularly Perturbed ◽  
Third Order ◽  
Diffusion Type ◽  
Convection Diffusion ◽  
Delay Differential

In this paper, a fitted finite difference method on Shishkin mesh is suggested to solve a class of third order singularly perturbed boundary value problems for ordinary delay differential equations of convection-diffusion type. Numerical solution converges uniformly to the exact solution. The order of convergence of the numerical method is almost first order. Numerical results are provided to illustrate the theoretical results.

scholarly journals Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
P. Hammachukiattikul ◽  
E. Sekar ◽  
A. Tamilselvan ◽  
R. Vadivel ◽  
N. Gunasekaran ◽  
...  
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Shishkin Mesh ◽  
Singularly Perturbed ◽  
Diffusion Type ◽  
Convection Diffusion ◽  
Discrete Norm ◽  
Difference Methods ◽  
Second Order Convergence ◽  
Delay Differential

In this paper, we consider a class of singularly perturbed advanced-delay differential equations of convection-diffusion type. We use finite and hybrid difference schemes to solve the problem on piecewise Shishkin mesh. We have established almost first- and second-order convergence with respect to finite difference and hybrid difference methods. An error estimate is derived with the discrete norm. In the end, numerical examples are given to show the advantages of the proposed results (Mathematics Subject Classification: 65L11, 65L12, and 65L20).

scholarly journals A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations

2020 ◽  
Vol 5 (1) ◽  
pp. 425-436 ◽  
Author(s):  
Fevzi Erdogan ◽  
Mehmet Giyas Sakar ◽  
Onur Saldır
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Delay Differential Equations ◽  
Perturbation Parameter ◽  
Shishkin Mesh ◽  
Singularly Perturbed ◽  
Initial Value ◽  
Uniformly Convergent ◽  
Delay Differential

AbstractThe purpose of this paper is to present a uniform finite difference method for numerical solution of a initial value problem for semilinear second order singularly perturbed delay differential equation. A numerical method is constructed for this problem which involves appropriate piecewise-uniform Shishkin mesh on each time subinterval. The method is shown to uniformly convergent with respect to the perturbation parameter. A numerical experiment illustrate in practice the result of convergence proved theoretically.

scholarly journals Fitted Operator Finite Difference Method for Singularly Perturbed Parabolic Convection-Diffusion Type

2021 ◽  
Vol 5 (1) ◽  
pp. 1-14
Author(s):  
Tesfaye Aga Bullo ◽  
Gemechis File Duressa
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Singularly Perturbed ◽  
Diffusion Type ◽  
Spatial Direction ◽  
Convection Diffusion ◽  
Backward Euler ◽  
Numerical Experimentation ◽  
Fitted Operator

In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson extrapolation method is applied on the time direction and the fitted operator finite difference method on the spatial direction is used, on the uniform grids. The stability and consistency of the method were established very well to guarantee the convergence of the method. Numerical experimentation is carried out on model examples, and the results are presented both in tables and graphs. Further, the present method gives a more accurate solution than some existing methods reported in the literature.

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