Asymptotic Initial Value Technique for singularly perturbed convection–diffusion delay problems with boundary and weak interior layers

An iterative numerical method for singularly perturbed reaction–diffusion equations with negative shift

“…Using the basic idea used in [14] for the continuous maximum principle and the discrete test function given by, S(x i ) = 1 + x i , ∀x i ∈ Ω N , the above theorem can be…”

“…In fact, Fevzi Erdogan [4] proposed an exponentially fitted operator method for singularly perturbed first order delay differential equations, Kadalbajoo and Sharma [5]- [7] and Jugal Mohapatra and Natesan [8] proposed few numerical methods for SPDDEs with small delays. Subburayan and Ramanujam [9]- [14] suggested numerical methods named as initial value technique and asymptotic numerical method for singularly perturbed delay differential equations of reaction-diffusion type as well as convection-diffusion type. Serge Nicaise and Christos Xenophontos [15], developed a hp-version finite element method to find an approximation to a solution of the singularly perturbed second order differential equation with a constant delay.…”

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

“…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.…”

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

“…In [4,16,17] have been considered some asymptotic analysis of boundary value problems for second order singularly perturbed differential-difference equations and some numerical techniques for solving of this type of problems with large and small shifts were considered in [12,14,18] and references therein. Particularly, reproducing kernel method [12], initial value technique [25], some special finite element method [23,26] have been used for solving these problems.…”