Treatment a New Approximation Method and Its Justification for Sturm–Liouville Problems

In this paper, we propose a new approximation method (we shall call this method as α-parameterized differential transform method), which differs from the traditional differential transform method in calculating the coefficients of Taylor polynomials. Numerical examples are presented to illustrate the efficiency and reliability of our own method. Namely, two Sturm–Liouville problems are solved by the present α-parameterized differential transform method, and the obtained results are compared with those obtained by the classical DTM and by the analytical method. The result reveals that α-parameterized differential transform method is a simple and effective numerical algorithm.