A parameter uniform difference scheme for parabolic partial differential equation with a retarded argument

A Robust numerical approach for singularly perturbed time delayed parabolic partial differential equations

“…From [8] it is easy to obtain Theorem 2.1. There exist a number C independent of such that for all sufficiently small positive values of the following relations hold:…”

Numerical solutions of a system of singularly perturbed reaction-diffusion problems

“…for some fixed step size h. The unknown coefficients c i j in relation (14) are determined by orthogonalizing the residual…”

“…Remark 3.1. Notice that the approach in the Sinc method is to select the basis functions so that each S j in (14) satisfies the homogeneous boundary conditions, if instead of homogeneous boundary conditions given in (1), the following nonhomogeneous boundary conditions are specified…”

“…Das and Natesan [12] considered a uniformly convergent hybrid scheme for singularly perturbed system of reaction-diffusion based on cubic spline approximation. We can point out to many other efficient methods for solving system of singularly perturbed equations as [4], [6], [7], [13], [14], [16], [17], [18], [24], [34], [37] and [38].…”

High order parameter-uniform discretization for singularly perturbed parabolic partial differential equations with time delay

“…In the direction of numerical study of singularly perturbed partial differential equations with time delay, much can be seen in [7][8][9][10], and the references therein. In particular for our model problem (3)- (5), the authors in [7,8] designed parameter uniform numerical methods using the fitted mesh and fitted operator approach, respectively, which results in uniform convergence of first order in time and second order in spatial direction.…”