A class of singularly perturbed two-point boundary-value problems for second-order ordinary differential equations arising in chemical reactor theory is considered. In order to solve them numerically, a method is suggested in which the given interval (the domain of the definition of the differential equation) is divided into two subintervals called inner and outer regions. In the inner region a...

In this paper we study a class of numerical methods to solve a singularly perturbed two-point boundary value problem. Our schemes arise as result of choosing an appropriate basis for the solution, as well as making use of collocation. It is possible to obtain arbitrarily high-order methods. We note that, in some cases (constant coefficients), we obtain the exact solution. Particular attention i...

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 brief note, we study the problem of asymptotic behavior solutions for non-resonant, singularly perturbed linear Neumann boundary value problems εy″+ky=f(t), y′(a)=0, y′(b)=0, k>0, with an indication possible extension to more complex cases. Our approach is based on analysis integral equation associated problem.

This paper is concerned with a class of singularly perturbed systems of two conservation laws. A small perturbation parameter is introduced in the dynamics and the boundary conditions. By setting the perturbation parameter to zero, the singularly perturbed system of conservation laws can be treated as two subsystems of one conservation law: the reduced system and the boundary-layer system. The ...

* Correspondence: [email protected] School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, People’s Republic of China Abstract Based on the method of differential inequalities, by constructing the upper ad lower solutions suitably, delayed phenomenon of loss of stability of solutions in a secondorder quasi-linear singularly perturbed Dirichlet boundary value problem ...

In this article a numerical method involving classical finite difference scheme on non-uniform grid is constructed for a singularly perturbed convection-diffusion boundary value problem with two small parameters affecting the convection and diffusion terms. The scheme has been analyzed for uniform convergence with respect to both singular perturbation parameters. To support the theoretical erro...