Chebyshev approximation to the solution of a singularly perturbed problem with nonlocal boundary conditions

Abstract

A singularly perturbed problem, described by the second order differential equation with nonlocal boundary conditions is considered. The solution is constructed as a sum of the exact solution of the reduced problem and the layer solutions, approximated by the truncated Chebyshev series upon the layer subintervals. A special procedure, adapted to the character of the boundary layer type, is applied to determine the layer subintervals. The coefficients of Chebyshev series solution are obtained using the collocation method. Two different techniques are applied to construct the upper bound for the error functions. A numerical example is included.

Keywords:

• Singular perturbation
• nonlocal conditions
• pseudo-spectral approximation
• numerical layer length