On the solution of singularly perturbed boundary value problems by a chebyshev method

Abstract

The approximate solution of a boundary value problem with a small parameter affecting the highest derivative of the differential equation is described. The approximate solution is expanded in terms of powers of the small parameter ∊ whose coefficients are unknown functions of the independent variable x. The resulting system of “numerically simpler” differential equations for the unknown coefficients of the expansion is solved using finite difference methods of order two and four. Numerical examples are given to illustrate the effectiveness of the methods.

Keywords: Finite difference methods; stiffness; Chebyshev method; asymptotic expansion; Gaussian elimination process; standard collocation method

Keywords:

• Finite difference methods
• stiffness
• Chebyshev method
• asymptotic expansion
• Gaussian elimination process
• standard collocation method

^∗Corresponding author.

^∗Corresponding author.

Notes

^∗Corresponding author.