Asymptotic stability in singular perturbation problems. II: Problems having matched asymptotic expansion solutions

Asymptotic - Numerical Method for Third-Order Singular Perturbation Problems

In this paper, a class of third order singularly perturbed boundary value problems with suitable boundary conditions is considered. The third order boundary value problem is transformed to asymptotically equivalent second order boundary value problem. This problem is solved efficiently by using fitted Numerov method. Linear and non-linear examples are solved to illustrate the method and relativ...

Asymptotic Solutions of Singular Perturbation Problems for Linear Differential Equations of Elliptic Type

Asymptotic Expansion of Solutions to Nonlinear Elliptic Eigenvalue Problems

We consider the nonlinear eigenvalue problem −∆u+ g(u) = λ sinu in Ω, u > 0 in Ω, u = 0 on ∂Ω, where Ω ⊂ RN (N ≥ 2) is an appropriately smooth bounded domain and λ > 0 is a parameter. It is known that if λ 1, then the corresponding solution uλ is almost flat and almost equal to π inside Ω. We establish an asymptotic expansion of uλ(x) (x ∈ Ω) when λ 1, which is explicitly represented by g.

Asymptotic Notation. Part II: Examples and Problems

The widely used textbook by Brassard and Bratley [2] includes a chapter devoted to asymptotic notation (Chapter 3, pp. 79–97). We have attempted to test how suitable the current version of Mizar is for recording this type of material in its entirety. This article is a follow-up to [11] in which we introduced the basic notions and general theory. This article presents a Mizar formalization of ex...

The Method of Asymptotic Inner Boundary Condition for Singular Perturbation Problems

The method of Asymptotic Inner Boundary Condition for Singularly Perturbed Two-Point Boundary value Problems is presented. By using a terminal point, the original second order problem is divided in to two problems namely inner region and outer region problems. The original problem is replaced by an asymptotically equivalent first order problem and using the stretching transformation, the asympt...