SPECTRAL-GRID APPROXIMATION OF A BOUNDARY VALUED PROBLEMFOR A FOURTH-ORDER SINGULARLY PERTURBED EQUATION

Abstract

Many studies devoted to solving boundary value problems for singularly perturbed differentialequations propose the use of nonuniform and adaptive meshes in order to localize the boundarylayer. However, the construction of such meshes generally requires the use of specific mappings,whose design can be associated with considerable difficulties and may lead to a significantincrease in the number of arithmetic operations. In this paper, the numerical modeling of aboundary value problem for a fourth-order singularly perturbed differential equation using thespectral-grid method is considered. First, the convergence of the spectral-grid method istheoretically justified, and estimates for the rate of convergence are obtained. Then, theconsidered problem is approximated using the spectral-grid method, and a correspondingsolution algorithm is developed.