A new kind of numerical method based on rational spectral collocation with the sinh transformation is presented for solving parameterized singularly perturbed two-point boundary value problems with one boundary layer. By means of the sinh transformation, the original Chebyshev points are mapped onto the transformed ones clustered near the singular points of the problem. The results from asympto...

The method of Asymptotic Inner Boundary Condition for Singularly Perturbed Two-Point Boundary value Problems is presented. By using a terminal point, the original second order problem is divided in to two problems namely inner region and outer region problems. The original problem is replaced by an asymptotically equivalent first order problem and using the stretching transformation, the asympt...

we consider the numerical approximation of a singularly perturbed reaction-diffusion problem over a square. Two different. approaches are compared namely: adaptive isotropic mesh refinement and anisotropic mesh refinement. Thus, we compare the h-refinement and the Shishkin mesh approaches numerically with PLTMG software [l]. It is shown how isotropic elements lead to over-refinement. and how an...

The regularization method for singularly perturbed problems of S. A. Lomov is generalized to constructing the asymptotics solution first boundary value problem systems differential equations parabolic type with a small parameter at all derivatives.It shown that contains n exponential, 2n and angle layer functions. exponential function describes along t = 0, x 0 1 described by

A coupled system of two singularly perturbed linear reaction–diffusion two-point boundary value problems is examined. The leading term of each equation is multiplied by a small positive parameter, but these parameters may have different magnitudes. The solutions to the system have boundary layers that overlap and interact. The structure of these layers is analysed, and this leads to the constru...

In this paper, in order to numerically solve for multiple positive solutions to a singularly perturbed Neumann boundary value problem in mathematical biology and other applications, a local minimax method is modified with new local mesh refinement and other strategies. Algorithm convergence and other related properties are verified. Motivated by the numerical algorithm and convinced by the nume...

REPORTRAPPORT Discrete approximations for singularly perturbed boundary value problems with parabolic layers Abstract Singularly perturbed boundary value problems for equations of elliptic and parabolic type are studied. For small values of the perturbation parameter, parabolic boundary layers appear in these problems. If classical discretisation methods are used, the solution of the nite diier...

The error generated by the classical upwind finite difference method on a uniform mesh, when applied to a class of singularly perturbed model ordinary differential equations with a singularly perturbed Neumann boundary condition, tends to infinity as the singular perturbation parameter tends to zero. Note that the exact solution is uniformly bounded with respect to the perturbation parameter. F...