Numerical method for a singularly perturbed convection–diffusion problem with delay

A parameter uniform numerical method for singularly perturbed delay problems with discontinuous convection coefficient

“…Again applying the result given in [9, Theorem 2.1] on [1,2], then we get ϕ ± 2 (x) ≥ 0. Using the procedure adopted in [7,Lemma 4], one can prove the rest of this theorem.…”

“…But in the recent years, there has been growing interest in this area. The authors of [12,6,16,1,2] suggested some numerical methods for singularly perturbed delay differential equations with continuous data. Recently few authors in [20,21,17] suggested some numerical method for singularly perturbed delay differential equations with discontinuous data.…”

On adaptive mesh for the initial boundary value singularly perturbed delay Sobolev problems

“…Singularly perturbed partial differential equations relate an unknown function to its derivatives evaluated at the same instance. We can see these types of problems in [32][33][34][35][36][37][38]. Singularly perturbed partial differential equations have been studied extensively by many authors and developed thoroughly over the recent decades [29,30].…”

“…But, when the delay is of big order of the singular perturbation parameter, the use of Taylor's series expansion for the term containing delay may lead to a bad approximation. We can see these types of problems in [32][33][34][35][36][37][38]. In this article, we suppose that r > 0 the delay parameter is big and proposes a special method for discretization of continuous time-delay.…”

Numerical Solution of a Boundary Value Problem Including Both Delay and Boundary Layer

“…i (k = 1, 2, 3) separately. Let us first proves bound for R (1) i . Using interpolating quadrature formula on interval (x i−1 , x i+1 ) with respect to points x i , x i+1 with remainder term in integral form we can write…”