Parameterized Differential Transform Method and Its Application to Boundary Value Transmission Problems

Abstract

In this study, we developed a new modification of the well-known differential transform method (DTM) that differs from the classical one by the algorithm for calculating the coefficients of an approximate solution given as a series. The proposed new algorithm we will call α-parameterized DTM (α-p DTM,for short). By using the proposed α-p DTM, we solve the boundary value transmission problem for the third-order differential equation. For the same problem, an approximate solution is also found using also the classical DTM. The solutions obtained were compared graphically.