Uniform numerical method for singularly perturbed delay differential equations

Uniform difference method for parameterized singularly perturbed delay differential equations

“…After establishing the uniformly boundness in ε of u(t) ∞ and |λ| , the proof of (2.3) is almost identical to that of [2].…”

“…Hence, if denote by τ (1) p and τ (2) p the stepsizes in [r p−1 , σ p ] and [σ p , r p ] respectively, we have…”

“…Finally, in Section 5, we formulate the iterative algorithm for solving the discrete problem and present numerical results which validate the theoretical analysis computationally. The technique to construct discrete problem and error analysis for approximate solution is similar to those in [1,2].…”

Fitted finite difference method for singularly perturbed delay differential equations

“…One of the simplest ways to derive such methods consists of using exponentially fitted difference schemes (see, e.g., [8][9][10][11][12] for motivation for this type of mesh). In the direction of numerical treatment for first order singularly perturbed delay differential equations, several can be seen in [13][14][15][16]. The singular perturbation analysis of boundary-value problem for differential-difference equations with small shifts has been given by Lange and Miura [17][18][19].…”

A Parameter Robust Method for Singularly Perturbed Delay Differential Equations

“…Such problems arise in the mathematical modeling of various practical phenomena, for example, in population dynamics 4 , the study of bistable devices 5 , description of the human pupil-light reflex 6 , and variational problems in control theory 7 . In the direction of numerical study of singularly perturbed delay differential equation, much can be seen in [8][9][10][11][12][13][14][15][16] .…”