Finite difference scheme for third order singularly perturbed delay differential equation of convection diffusion type with integral boundary condition

2019 ◽  
Vol 61 (1-2) ◽  
pp. 73-86 ◽  
Author(s):  
Elango Sekar ◽  
Ayyadurai Tamilselvan
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Finite Difference ◽  
Difference Scheme ◽  
Singularly Perturbed ◽  
Third Order ◽  
Diffusion Type ◽  
Integral Boundary ◽  
Convection Diffusion ◽  
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 Finite difference scheme for singularly perturbed reaction diffusion problem of partial delay differential equation with nonlocal boundary condition

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sekar Elango ◽  
Ayyadurai Tamilselvan ◽  
R. Vadivel ◽  
Nallappan Gunasekaran ◽  
Haitao Zhu ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Difference Scheme ◽  
Boundary Layers ◽  
Finite Difference Scheme ◽  
Nonlocal Boundary ◽  
Singularly Perturbed ◽  
Uniform Mesh ◽  
Integral Boundary ◽  
Delay Term

AbstractThis paper investigates singularly perturbed parabolic partial differential equations with delay in space, and the right end plane is an integral boundary condition on a rectangular domain. A small parameter is multiplied in the higher order derivative, which gives boundary layers, and due to the delay term, one more layer occurs on the rectangle domain. A numerical method comprising the standard finite difference scheme on a rectangular piecewise uniform mesh (Shishkin mesh) of $N_{r} \times N_{t}$ N r × N t elements condensing in the boundary layers is suggested, and it is proved to be parameter-uniform. Also, the order of convergence is proved to be almost two in space variable and almost one in time variable. Numerical examples are proposed to validate the theory.

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