Related papers: A Mixed Finite Element Method for Singularly Pertu…
This paper introduces a numerical approach to solve singularly perturbed convection diffusion boundary value problems for second-order ordinary differential equations that feature a small positive parameter {\epsilon} multiplying the…
In this paper, a boundary value problem for a singularly perturbed linear system of two second order ordinary differential equations of convection- diffusion type is considered on the interval [0, 1]. The components of the solution of this…
We consider fourth order singularly perturbed boundary value problems with two small parameters, and the approximation of their solution by the $hp$ version of the Finite Element Method on the {\emph{Spectral Boundary Layer}} mesh from…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
A system of singularly perturbed ordinary differential equations of first order with given initial conditions is considered. The leading term of each equation is multiplied by a small positive parameter. These parameters are assumed to be…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective…
This work develops an epsilon-uniform finite element method for singularly perturbed boundary value problems. A surprising and remarkable observation is illustrated: By moving one node arbitrarily in between its adjacent nodes, the new…
We consider the singularly perturbed fourth-order boundary value problem $\varepsilon ^{2}\Delta ^{2}u-\Delta u=f $ on the unit square $\Omega \subset \mathbb{R}^2$, with boundary conditions $u = \partial u / \partial n = 0$ on $\partial…
In the present paper we consider the numerical solving of a semilinear singular--perturbation reaction--diffusion boundary--value problem having boundary layers. A new difference scheme is constructed, the second order of convergence on a…
In this paper, we investigate a weakly coupled system of singularly perturbed linear reaction-diffusion equations with Robin boundary conditions, where the leading terms are multiplied by small positive parameters that may differ in…
A singularly perturbed linear system of second order partial differential equations of parabolic reaction-diffusion type with given initial and boundary conditions is considered. The leading term of each equation is multiplied by a small…
In this article, a parameter-uniform numerical method is presented to solve one-dimensional singularly perturbed parabolic convection-diffusion turning point problem exhibiting two exponential boundary layers. We study the asymptotic…
In this paper we are considering a semilinear singular perturbation reaction -- diffusion boundary value problem, which contains a small perturbation parameter that acts on the highest order derivative. We construct a difference scheme on…
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…
The singularly perturbed reaction-diffusion problem $\varepsilon^2\Delta^2 u - \mathrm{div}\left(c\nabla u\right) = f$ is considered on the unit square $\Omega$ in $\mathbb{R}^2$ with homogenous Dirichlet boundary conditions. Its solution…
In this paper, a parameter-uniform fitted mesh finite difference scheme is constructed and analyzed for a class of singularly perturbed interior turning point problems. The solution of this class of turning point problem possess two outflow…
A series of robust and optimal mixed methods based on two mixed formulations of the fourth-order elliptic singular perturbation problem are developed in this paper. First, a mixed method based on a second-order system is proposed without…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
In this paper, we propose a finite element method to study the problem ofcredit rating migration problem narrowed to a free boundary problem. Freeboundary indeed separates the high and low rating region for a firm andcauses some…