Abstract In this paper, we have studied a method based on exponential splines for numerical solution of singularly perturbed two parameter boundary value problems. The problem is solved Shishkin mesh by using splines. Numerical results are tabulated different values the perturbation parameters. From results, it found that approximates exact very well.

In this paper, we consider a second-order singularly perturbed differential-difference equations with mixed delay and advance parameters. At first, we approximate the model problem by an upwind finite difference scheme on a Shishkin mesh. We know that the upwind scheme is stable and its solution is oscillation free, but it gives lower order of accuracy. So, to increase the convergence, we propo...

The purpose of this paper is to present a uniform finite difference method for numerical solution of nonlinear singularly perturbed convection-diffusion problem with nonlocal and third type boundary conditions. The numerical method is constructed on piecewise uniform Shishkin type mesh. The method is shown to be convergent, uniformly in the diffusion parameter ε, of first order in the discrete ...

In this paper, we deal with a singularly perturbed parabolic convection-diffusion problem. Shishkin mesh and hybrid third-order finite difference scheme are adopted for the spatial discretization. Uniform backward Euler used temporal Furthermore, preconditioning approach is also to ensure uniform convergence. Numerical experiments show that method first-order accuracy in time almost space.

We examine a time dependent singularly perturbed convection-diffusion problem, where the convective coefficient contains an interior layer. A smooth transformation is introduced to align the grid to the location of the interior layer. A numerical method consisting of an upwinded finite difference operator and a piecewise-uniform Shishkin mesh is constructed in this transformed domain. Numerical...

This paper considers a simple central difference scheme for a singularly perturbed semilinear reaction–diffusion problem, which may have multiple solutions. Asymptotic properties of solutions to this problem are discussed and analyzed. To compute accurate approximations to these solutions, we consider a piecewise equidistant mesh of Shishkin type, which contains O(N) points. On such a mesh, we ...

In this article, we consider singularly perturbed reaction-diffusion Robin boundary-value problems. To solve these problems we construct a numerical method which involves both the cubic spline and classical finite difference schemes. The proposed scheme is applied on a piece-wise uniform Shishkin mesh. Truncation error is obtained, and the stability of the method is analyzed. Also, parameter-un...

In this paper, a singularly perturbed system of reaction–diffusion Boundary Value Problems (BVPs) is examined. To solve such a type of problems, a Modified Initial Value Technique (MIVT) is proposed on an appropriate piecewise uniform Shishkin mesh. The MIVT is shown to be of second order convergent (up to a logarithmic factor). Numerical results are presented which are in agreement with the th...

Abstract. In this paper, a bilinear Streamline-Diffusion finite element method on Bakhvalov-Shishkin mesh for singularly perturbed convection – diffusion problem is analyzed. The method is shown to be convergent uniformly in the perturbation parameter ǫ provided only that ǫ ≤ N. An O(N(lnN)) convergent rate in a discrete streamline-diffusion norm is established under certain regularity assumpti...

We consider the numerical solution of a singularly perturbed two-dimensional reactiondiffusion problem by a multiscale sparse grid finite element method. A Shishkin mesh which resolves the boundary and corner layers, and yields a parameter robust solution, is used. Our analysis shows that the method achieves essentially the same accuracy as the standard Galerkin finite element method, but does ...