Restrictive Taylor's approximation for solving convection-diffusion equation

In this paper, we shall develop a new explicit method for solve the convection-diffusion equation, which will exhibit several advantageous features: highly accurate, fast and with good results whatever the exact solution is too large. The stability region is discussed. The error upper bound is proved. The obtained results for a test problem compared with the exact solution and its Douglas approximation, it proves the mentioned advantages. © 2002 Elsevier Inc. All rights reserved.