[PDF] Top 20 Isogeometric analysis for singularly perturbed problems in 1-D: error estimates

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

... differential problems (see, ...convergence analysis have been given in Section ...the error analysis for the approximate solution are similar to those in ... See full document

... of singularly perturbed ...of singularly perturbed boundary-value problems, the choice of a proper method for the construction of solutions or their asymptotic approximations without ... See full document

... The discrete Schwarz method that we consider is a domain decomposition version of the numerical method of [8], where problem (1.1), (1.5) was posed in a smooth two-dimensional domain, and it was shown that one gets ... See full document

... posteriori error estimation, much attention focuses on specifying the error ...for singularly perturbed problems, the error constant might blow up as ε becomes small, and hence ... See full document

... In the present paper we discretize 1.1-1.2 using a numerical method which is composed of an implicit finite difference scheme on special Bakhvalov meshes for the numerical solution on each timesubinterval. In Section 2, ... See full document

... self-adjoint singularly perturbed bound- ary value ...Tables 1 and ...Figs. 1 and 2, the pro- posed method approximates the exact solution very well for h ≥ ε , for which most of the current ... See full document

... The paper is organized as follows: in section 2, we give some properties of the solution of (1.1) and in section 3, we state the difference approximation Il’in scheme. In section 4, we analyze the error of Il’in ... See full document

... The analysis of the formal asymptotic solution of (1) in this paper follows that of a linear version studied in ...For singularly perturbed Volterra equa- tions with weakly singular kernels ... See full document

... life problems governed by ODEs and/or by ...second-order singularly-perturbed delay differential ...these problems to those of solving a system of algebraic equations, thus greatly simplifying ... See full document

... In Section 2, we introduce the classical nonlinear finite difference schemes for the nu- merical solution of (1.1) and (1.2). Iterative methods by which each of these schemes may be solved are presented in [3, 4]. From an ... See full document

... C 1 [ ] 0, T ×  for which problem (1), (2) is ...of problems have also been considered. The qualitative analysis of singular perturbation situations have always been far from trivial because ... See full document

... asymptotic analysis for problems of type ...pointwise estimates of solution ...= 1, and an exponential boundary layer along the outflow boundary x = ...= 1, then solutions also exhibit ... See full document

... Isogeometric Analysis is approached, using continuous or discontinuous Ga- lerkin method. In the context of space semidiscretization by discontinuous Ga- lerkin methods, explicit RK schemes are used to ... See full document

... of problems. The qualitative analysis of singular perturbation situations has always been far from trivial because of the boundary layer behavior of the ...cases, problems depend on a small parameter ... See full document

... qualitative analysis geometric method theory ...structure problems, we just start from some particular class of singularly perturbed system and are trying to develop some approach to construct ... See full document

... interval analysis perspective to evaluate the range of the solution for the singularly perturbed two-point boundary value problems with uncertain ...Sensitivity analysis has been ... See full document

... Recently, some efforts have been put into developing spectral methods for solving FOCPs. For instance, a numerical direct method based on the Legendre orthonormal ba- sis and operational matrix of Riemann-Liouville ... See full document

... Note that we do not correct the boundary conditions up to arbitrarily large values of i. We make use of this condition only for the considered finite number of indices. Additionally, the boundary correction functions are ... See full document

... treated singularly perturbed delay differential equation of second order using B-spline collocation ...handle singularly perturbed ...considered problems is not known so the maximum ... See full document