Almost second-order uniformly convergent numerical method for singularly perturbed convection–diffusion–reaction equations with delay

Boundary Layer Resolving Exact Difference Scheme for Solving Singularly Perturbed Convection-Diffusion-Reaction Equation

“…Using Shishkin decomposition in [12,23], the solution u(x, t) of ( 1) can be decomposed into regular and singular component as follows:…”

“…Here, we decompose the numerical solution U i,j+1 into regular and singular components using the Shishkin decomposition in [12] as follows:…”

“…Standard numerical methods on uniform mesh fail to give accurate results and create oscillations in the computed solution due to the presence of a small perturbation parameter (ε) on the difusion term [11,12]. To avoid the oscillations and obtain an accurate solution using the standard numerical methods on uniform mesh, it requires an unacceptably large number of mesh points when ε is very small.…”

“…Nowadays, the numerical treatment of singularly perturbed convection-difusion-equations has attracted great attention [4]. Te authors in [12][13][14][15][16] used the ftted mesh methods for solving diferent classes of singularly perturbed problems, and the authors in [17][18][19] used the ftted operator methods for developing uniformly convergent numerical schemes.…”

A fitted numerical method for a singularly perturbed Fredholm integro-differential equation with discontinuous source term

“…In [16] the authors worked on a delay differential equation with exponentially fitted methods. In [15] the author proved second order convergence for singularly perturbed delay differential equations using fitted mesh method. Amiraliyev et al [2] showed that first-order convergence on a uniform mesh was obtained globally for a first-order equation considering an exponential fitting approach.…”