A Constructive Theorem of Existence and Uniqueness for the Problem\documentclass{article}\pagestyle{empty}\begin{document}$ y' = f(x,y,\lambda),y(a) = \alpha,y\left( b\right) = \beta $\end{document}

A parameter uniform difference scheme for the parameterized singularly perturbed problem with integral boundary condition

“…The values of ε and N , for which we solve the test problem, are ε = 2 -i , i = 0, 4,8,12,16; N = 64, 128, 256, 512, 1024. From Tables 1 and 2 we observe that ε-uniform experimental rates of convergence monotonically increase towards one, which is in agreement with the theoretical rate given by Theorem 3.1.…”

“…Such problems arise in physical chemistry and physics, describing the exothermic and isothermal chemical reactions, the steady-state temperature distributions, the oscillation of a mass attached by two springs leading to a differential equation with a parameter [5,11,12]. An overview of some existence and uniqueness results and applications of parameterized equations may be obtained, for example, in [11][12][13][14](see also references therein). In [11,12,14,15], the authors have also considered some approximating aspects of this kind of problems.…”

“…An overview of some existence and uniqueness results and applications of parameterized equations may be obtained, for example, in [11][12][13][14](see also references therein). In [11,12,14,15], the authors have also considered some approximating aspects of this kind of problems. But in the above-mentioned papers, algorithms are only concerned with the regular cases (i.e., when the boundary layers are absent).…”

Finite‐difference method for parameterized singularly perturbed problem

“…Under the above conditions, there exists a unique solution to problem (1.1), (1.2) (see [7,12]). An overview of some existence and uniqueness results and applications of parameterized equations may be obtained, for example, in [6,7,8,9,12,13,15,16]. In [7,9,12], have also been considered some approximating aspects of this kind of problems.…”

Asymptotic Estimates for Second-Order Parameterized Singularly Perturbed Problem

“…An overview of some existence and uniqueness results and applications of parameterized equations may be obtained, for example, in [1]- [10]. In [11]- [14], some approximating aspects of this kind of problems have also been considered.…”