[PDF] Top 20 A second-order overlapping Schwarz method for a 2D singularly perturbed semilinear reaction-diffusion problem

... discrete Schwarz method that we consider is a domain decomposition version of the numerical method of [8], where problem ...gets second-order convergence in the discrete maximum ... See full document

... these difficulties is given by Figure 2.1, where a standard 3-point difference scheme produces unstable solutions on both an equidistant mesh and an appropriate Shishkin mesh (compare these results with the solutions of the ... See full document

... Singularly perturbed second-order boundary value problem occur very frequently in fluid motion, chemical reactor theory, elasticity, diffusion in polymer, ... See full document

... of problem have also been considered 13, ...three-point reaction-diffusion problem have been studied in ...difference method, which is first-order convergent, on an S-mesh Shishkin type ... See full document

... to second order ...for singularly perturbed higher order differential ...the order of original differential equa- tion is affected if sets ε = 0 ...The singularly ... See full document

... difference method for solving a singularly perturbed reaction-diffusion problem with a discontinuous source ...a second-order differ- ence scheme on an additional refined mesh ... See full document

... A singularly perturbed boundary value problem for a linear system of two parabolic second order delay differential equations of reaction-diffusion type is ...highest ... See full document

... of singularly perturbed second order ordinary differential equations of reaction-diffusion type with Robin boundary conditions is ...numerical method for solving this ... See full document

... The paper is organized as follows. In section 2, we describe the numerical method, present our a posteriori error estimate in Theorem 2.1, and outline its proof. Next, in section 3, we establish some estimates for ... See full document

... components of the asymptotic expansion are given. We shall use these estimates in a forthcoming paper to derive a robust numerical method and establish its ε-uniform accuracy. Similar results have been obtained by ... See full document

... consider second order singularly perturbed problems (SPPs) in one- dimension, of reaction-convection-diffusion type, whose solution contains boundary layers; see, ...One ... See full document

... B C F ⋅ = (14) The B-spline function is a useful wavelet basis function, the stiffness matrix is sparse. When it is used as trial functions, which leads to a tri-diagonal linear system. Hence the wavelet collocation ... See full document

... [4] Feng, Z.S. (2003) Traveling Solitary Wave Solutions to the Generalized Boussinesq Equation. Wave Motion , 37, 17-23. https://doi.org/10.1016/S0165-2125(02)00019-7 [5] Song, C., Li, H. and Li, J. (2013) Initial ... See full document

... a singularly perturbed two-point boundary value problem with right end boundary layer in the interval ...given problem and finds the numerical ...this method on two linear examples with ... See full document

... Table 5.2. All execution times of this section have been rounded up to the nearest second. Each major cell corresponds to a certain nonlinear system (2.2) to be solved by algo- rithm (3.5)–(3.10). Within each ... See full document

... nonlinear singularly perturbed multi-point boundary value problem is given to illustrate the efficiency of the numerical method described ...the method are compared with the exact ... See full document

... the problem (.) on the bounded domain with ∂ of class C ∞ . In order to construct the formal asymptotic solution we need to propose suitable parameter transfor- ... See full document

... [11] S. Hemavathi, T. Bhuvaneswari, S. Valarmathi and J. J. H. Miller, “A Parameter Uniform Numerical Method for a System of Singularly Perturbed Ordinary Differential Equations,” Applied Mathematics ... See full document

... However, there are many practical situations in which the normal hyperbolicity of the reduced solutions lose. That is, in geometrical speaking, there exist turning points on the critical curve. The existence of turning ... See full document

... As was said before, we apply the method of lower and upper solutions to prove the existence of a solution for problem 1.1, 1.2 which converges uniformly to the solution u of the reduced problem i.e., ... See full document