scholarly journals Exponentially fitted finite difference method for singularly perturbed delay differential equations with integral boundary condition

2019 ◽  
Vol 11 (4) ◽  
pp. 476-493 ◽  
Author(s):  
Habtamu Garoma Debela ◽  
Gemechis File Duressa
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Difference Method ◽  
Delay Differential Equations ◽  
Singularly Perturbed ◽  
Integral Boundary ◽  
Exponentially Fitted ◽  
Delay Differential

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 Accelerated fitted operator finite difference method for singularly perturbed delay differential equations with non-local boundary condition

2020 ◽  
Vol 28 (1) ◽  
Author(s):  
Habtamu Garoma Debela ◽  
Gemechis File Duressa
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Singularly Perturbed ◽  
Local Boundary ◽  
Local Boundary Condition ◽  
Numerical Experimentation ◽  
Non Local ◽  
Delay Differential

Abstract In this paper, accelerated fitted finite difference method for solving singularly perturbed delay differential equation with non-local boundary condition is considered. To treat the non-local boundary condition, Simpson’s rule is applied. The stability and parameter uniform convergence for the proposed method are proved. To validate the applicability of the scheme, two model problems are considered for numerical experimentation and solved for different values of the perturbation parameter ε and mesh size h. The numerical results are tabulated in terms of maximum absolute errors and rate of convergence, and it is observed that the present method is more accurate and ε-uniformly convergent for h ≥ ε where the classical numerical methods fails to give good result, and it also improves the results of the methods existing in the literature.

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.

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