Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations | Zendy

P. Hammachukiattikul | Zendy; Sekar Elango | Zendy; A. Tamilselvan | Zendy; R. Vadivel | Zendy; N. Gunasekaran | Zendy; Praveen Agarwal | Zendy

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

Author(s) -

P. Hammachukiattikul,

Sekar Elango,

A. Tamilselvan,

R. Vadivel,

N. Gunasekaran,

Praveen Agarwal

Publication year - 2021

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2021/6636607

Subject(s) - mathematics , piecewise , finite difference method , singular perturbation , convergence (economics) , mathematics subject classification , uniform convergence , finite difference , differential equation , numerical analysis , finite difference scheme , norm (philosophy) , delay differential equation , class (philosophy) , convection–diffusion equation , mathematical analysis , discrete mathematics , computer network , bandwidth (computing) , artificial intelligence , computer science , political science , law , economics , economic growth

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).

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