A note on a parameterized singular perturbation problem

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.…”

“…Uniform convergent finite-difference schemes for solving parameterized singularly perturbed two-point boundary value problems have been considered in [8,10,[15][16][17][18][19][20][21][22] (see also references therein). In [8,10,16,17,19,20] authors used the boundary layer technique for solving an analogous problem. A methodology based on the homotopy analysis technique to approximate the analytic solution was investigated in [15,21,22].…”

Uniform difference method for parameterized singularly perturbed delay differential equations

“…Hence, if denote by τ (1) p and τ (2) p the stepsizes in [r p−1 , σ p ] and [σ p , r p ] respectively, we have…”

“…Finally, in Section 5, we formulate the iterative algorithm for solving the discrete problem and present numerical results which validate the theoretical analysis computationally. The technique to construct discrete problem and error analysis for approximate solution is similar to those in [1,2].…”

“…For a discussion of existence and uniqueness results and for applications of parameterized equations see, [10,[15][16][17] and references therein. A number of papers devoted to the approximating techniques to initial and boundary value problems, see for example [1,15,17,24]. But designed in the above-mentioned papers algorithms mainly focused on the stability of numerical methods to regular cases (i.e.…”