Uniformly convergent finite difference method for reaction-diffusion type third order singularly perturbed delay differential equation

2021 ◽  
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Delay Differential Equation ◽  
Reaction Diffusion ◽  
Singularly Perturbed ◽  
Third Order ◽  
Diffusion Type ◽  
Uniformly Convergent ◽  
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.

Numerical Dynamics of Nonstandard Finite Difference Method for Nonlinear Delay Differential Equation

2018 ◽  
Vol 28 (11) ◽  
pp. 1850133 ◽  
Author(s):  
Xiaolan Zhuang ◽  
Qi Wang ◽  
Jiechang Wen
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Delay Differential Equation ◽  
Difference Method ◽  
Discrete System ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay ◽  
Nonstandard Finite Difference

In this paper, we study the dynamics of a nonlinear delay differential equation applied in a nonstandard finite difference method. By analyzing the numerical discrete system, we show that a sequence of Neimark–Sacker bifurcations occur at the equilibrium as the delay increases. Moreover, the existence of local Neimark–Sacker bifurcations is considered, and the direction and stability of periodic solutions bifurcating from the Neimark–Sacker bifurcation of the discrete model are determined by the Neimark–Sacker bifurcation theory of discrete system. Finally, some numerical simulations are adopted to illustrate the corresponding theoretical results.

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 Quintic B-Spline Technique for Numerical Treatment of Third Order Singular Perturbed Delay Differential Equation

2019 ◽  
Vol 4 (6) ◽  
pp. 1471-1482
Author(s):  
Mandeep Kaur Vaid ◽  
Geeta Arora
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Singularly Perturbed ◽  
Uniform Mesh ◽  
Numerical Treatment ◽  
Spline Collocation ◽  
Third Order ◽  
B Spline ◽  
Collocation Technique ◽  
Delay Differential

In this paper, a class of third order singularly perturbed delay differential equation with large delay is considered for numerical treatment. The considered equation has discontinuous convection-diffusion coefficient and source term. A quintic trigonometric B-spline collocation technique is used for numerical simulation of the considered singularly perturbed delay differential equation by dividing the domain into the uniform mesh. Further, uniform convergence of the solution is discussed by using the concept of Hall error estimation and the method is found to be of first-order convergent. The existence of the solution is also established. Computation work is carried out to validate the theoretical results.

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