Solving systems of ordinary differential equations in unbounded domains by exponential Chebyshev collocation method

The purpose of this paper is to investigate the use of exponential Chebyshev collocation method for solving systems of linear ordinary differential equations with variable coefficients in unbounded domains, with most general form of conditions. The definition of the exponential Chebyshev (EC) functions allows us to deal with systems of differential equations defined in the whole domain and with infinite boundaries without singularities or divergence. The method transforms the system of differential equations and the given conditions to block matrix equation with unknown EC coefficients. By means of the obtained matrix equations, a new system of equations which corresponds to the system of linear algebraic equations is gained. Numerical examples are included to illustrate the validity and applicability of the method.