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.

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 propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. a numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. truncation errors are derived for both continuous and discontinuous problems. parameter uni...

In this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. A numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. Truncation errors are derived for both continuous and discontinuous problems. Parameter uni...

An overlapping Schwarz domain decomposition is applied to a semilinear reaction-diffusion equation posed in a smooth two-dimensional domain. The problem may exhibit multiple solutions; its diffusion parameter ε2 is arbitrarily small, which induces boundary layers. The Schwarz method invokes a boundary-layer subdomain and an interior subdomain, the narrow subdomain overlap being of width O(ε| ln...

A finite-element approach, based on cubic B-spline collocation, is presented for the numerical solution of Troesch’s problem. The method is used on both a uniform mesh and a piecewise-uniform Shishkin mesh, depending on the magnitude of the eigenvalues. This is due to the existence of a boundary layer at the right endpoint of the domain for relatively large eigenvalues. The problem is also solv...

A finite element method for a singularly perturbed convection-diffusion problem with exponential boundary layers is analysed. Using a mortaring technique we combine an anisotropic triangulation of the layer region (into rectangles) with a shape regular one of the remainder of the domain. This results in a possibly non-matching (and hybrid), but layer adapted mesh of Shishkin type. We study the ...

In the present paper we consider a boundary value problem on the semiaxis (0;∞) for a singularly perturbed parabolic equation with the two perturbation parameters 1 and 2 multiplying, respectively, the second and 5rst derivatives with respect to the space variable. Depending on the relation between the parameters, the di7erential equation can be either of reaction–di7usion type or of convection...

Two upwind finite difference schemes are considered for the numerical solution of a class of semilinear convection-diffusion problems with a small perturbation parameter ε and an attractive boundary turning point. We show that for both schemes the maximum nodal error is bounded by a special weighted `1-type norm of the truncation error. These results are used to establish ε-uniform pointwise co...

Numerical approximations to the solution of a linear singularly perturbed parabolic problem are generated using a backward Euler method in time and an upwinded finite difference operator in space on a piecewise-uniform Shishkin mesh for a convectiondiffusion problem. A proof is given to show first order convergence of these numerical approximations in appropriately weighted C-norm. Numerical re...