This paper is concerned with a semi-linear elliptic problem Robin boundary condition: style='text-indent:20px;'> \begin{document}$ \begin{equation} \left\{\begin{array}{lll} \varepsilon \Delta w-\lambda w^{1+\chi} = 0, &\text{in} \ \Omega\\ \nabla w \cdot \vec{n}+\gamma & \text{on} \partial \Omega \end{array}\right...

A class of singularly perturbed two point Boundary Value Problems (BVPs) of reaction-diffusion type for third order Ordinary Differential Equations (ODEs) with a small positive parameter (ε) multiplying the highest derivative and a discontinuous source term is considered. The BVP is reduced to a weakly coupled system consisting of one first order ordinary differential equation with a suitable i...

On the rectangular space-time domain G = D (0; T ] with the boundary S = GnG, where D = (0; d), we consider the Dirichlet problem for the singularly perturbed parabolic equation: " 2 @ @x a(x; t) @ @x u(x; t) ! ? c(x; t)u(x; t) ? p(x; t) @ @t u(x; t) = f(x; t); (1a) The perturbation parameter " may take any small positive value, say " 2 (0; 1]. If " = 0, the parabolic equation (1a) degenerates ...

Recommended by Donal O'Regan This paper is concerned with solving nonlinear singularly perturbed boundary value problems. Robust monotone iterates for solving nonlinear difference scheme are constructed. Uniform convergence of the monotone methods is investigated, and convergence rates are estimated. Numerical experiments complement the theoretical results.

A heterogeneous domain-decomposition method is presented for the numerical solution of singularly perturbed elliptic boundary value problems. The method, which is parallelizable at various levels, uses several ideas of asymptotic analysis. The subdomains match the domains of validity of the local [ “inner” and “outer”) asymptotic expansions, and cut-off functions are used to match solutions in ...

We study a singularly perturbed boundary value problrm in R”““: i =.f(s. J, E). cj= glx, .r, s), B,(s(w,), .tj(uo), E)=O, B,(.~(m,+to), ~(w,+oJ), E) =O. Given a candidate for the 0th order approximation which exhibits both boundary layers and interior layers, we present a complete procedure to compute higher order expansions and a procedure to compute the real solution near a truncated asymptot...

As Science & technology develop, many practical problems, such as the mathematical boundary layer theory or approximation of solution of various problems described by differential equations involving large or small parameters have become increasingly complex and therefore require the use of asymptotic methods. However, the theory of asymptotic analysis for differential operators has mainly been...

This paper extends the application of Differential Quadrature Method (DQM) for finding the numerical solution of general singularly perturbed two point boundary value problems with a boundary layer at right end point or both end point or at an internal point. The Differential Quadrature Method is an efficient descritization technique in solving initial and /or boundary value problems accurately...