Numerical modeling of the boundary value problem of an ordinary differential equation with a small parameter at the highest derivative by Chebyshev polynomials of the second kind

Abstract

In the present work the application of the spectral method with Chebyshev polynomials of the second kind is considered for solving a boundary value problem of an ordinary differential equation with a small parameter at the highest derivative. Numerical and graphical results illustrate the effectiveness of the applied method for various values of polynomials.

Keywords

• Small parameter
• Chebyshev polynomials
• Boundary conditions
• Polynomial nodes
• Spectral solution