TY - JFULL AU - M. F. Patricio and P. M. Rosa PY - 2007/10/ TI - The Differential Transform Method for Advection-Diffusion Problems T2 - International Journal of Mathematical and Computational Sciences SP - 420 EP - 425 VL - 1 SN - 1307-6892 UR - https://publications.waset.org/pdf/8361 PU - World Academy of Science, Engineering and Technology NX - Open Science Index 9, 2007 N2 - In this paper a class of numerical methods to solve linear and nonlinear PDEs and also systems of PDEs is developed. The Differential Transform method associated with the Method of Lines (MoL) is used. The theory for linear problems is extended to the nonlinear case, and a recurrence relation is established. This method can achieve an arbitrary high-order accuracy in time. A variable stepsize algorithm and some numerical results are also presented. ER -