Parameter-uniform hybrid difference scheme for solutions and derivatives in singularly perturbed initial value problems

Robust Numerical Method for Singularly Perturbed Convection-Diffusion Type Problems With Non-Local Boundary Condition

“…Some approaches for the numerical solution of singularly perturbed nonlocal boundary value problems have been proposed in [6,7,11,13,14,15,16,18] and [26]. Uniformly convergent numerical methods of order second and high for solving different singularly perturbed problems have been studied in [5,8,9,10,12,13,14,15,16,27] and [36]. To the best of our knowledge, the problem under consideration has not been done using nonstandard fitted finite difference method.…”

Exponential Fitted Operator Method for Singularly Perturbed Convection-Diffusion Type Problems with Nonlocal Boundary Condition

“…Some approaches for the numerical solution of singularly perturbed nonlocal boundary value problems have been proposed in [20][21][22][23][24][25][26][27][28]. Uniformly convergent numerical methods of order second and high for solving different singularly perturbed problems have been studied in [29][30][31][32][33][34]. To the best of our knowledge, the problem under consideration has not been done using the fitted operator method.…”

A higher order finite element method with modified graded mesh for singularly perturbed two‐parameter problems

“…In Cen et al 18 and Erdogan and Amiraliyev, 19 the authors deal with initial value problems involving two parameters. In Cen et al, 20 assumptions posed on the coefficients suggests that the differential operator does not satisfy the maximum principle. However, the problem can be transformed into a coupled system of first-order initial value problems.…”

“…Indeed, the transformed system is different from the one that meets the maximum principle. 21 A hybrid finite difference method over a Shishkin mesh is presented in Cen et al 20 This method is a combination of a second-order difference scheme on the fine mesh and the modified midpoint upwind scheme on a coarse mesh. With the help of truncation error estimate technique and using difference analog of Gronwall's inequality, it is proved that the method presented is second-order accurate.…”