A Numerical Scheme For Semilinear Singularly Perturbed Reaction-Diffusion Problems

Abstract

In this study we investigated the singularly perturbed boundary value problems for semilinear reaction-difussion equations. We have introduced a basic and computational approach scheme based on Numerov’s type on uniform mesh. We indicated that the method is uniformly convergence, according to the discrete maximum norm, independently of the parameter of ɛ. The proposed method was supported by numerical example.

Fourth-order fitted mesh scheme for semilinear singularly perturbed reaction–diffusion problems

“…This paper deals with singularly perturbed semilinear reaction–diffusion problem: subject to the conditions where is perturbation parameter, and are given constant numbers. Assume that the functions and the nonlinear term is given sufficiently smooth with [0,1], and for some constant to ensure the existence and unique solution with dual boundary layers near the two end points of the solution domain [ 14 ]. The reduced problem of Eq.…”

“…Quasilinearization technique used to transform the semilinear singularly perturbed reaction–diffusion problem into a sequence of linear equations, [ 14 ]. We choose a reliable initial approximation for the function in as: where and are arbitrary constants determined using Eq.…”

“…Recently, a numerical scheme for solving the semilinear singularly perturbed reaction–diffusion problems and a numerical technique for solving a class of nonlinear singularly perturbed boundary value problems have been presented respectively, in [ 2 , 14 ]. They have introduced a basic and computational approach scheme based on Numerov’s type on uniform mesh.…”

Numerical simulation of heat dissipation of surface mounted permanent magnet synchronous hub motor

“…Since the rotor can be regarded as a rotating cylinder when the motor is running, it can be calculated according to the calculation method of the surface heat dissipation coefficient of the rotating cylinder. When there is no flow in the axial direction, it can be calculated according to the relative motion of the flow over the large plane wall [16]. Due to the air winding near the outer surface of the motor rotor yoke, it can be calculated according to:…”

A New Parameter-Uniform Discretization of Semilinear Singularly Perturbed Problems

“…More recently, further works were completed on semilinear singularly perturbed scalar boundary value problems [24], scalar parabolic problems [25], or on systems of such problems [26][27][28][29]. Again, the methods adopted in these works are essentially the fitted finite difference methods based on Shishkin meshes.…”