Theoretical Analysis of the Exponential Transversal Method of Lines for the Diffusion Equation A. J. Salazar, 1 M. Raydan, 2 A. Campo 3 1 Department of Mechanical Engineering, University of Kentucky, Lexington, Kentucky 40506 2 Escuela de Computacion, Universidad Central de Venezuela, Apdo. Postal 47002, Caracas 1041-A, Venezuela 3 College of Engineering, Idaho State University, Pocatello, Idaho 83209 Received November 3, 1997; accepted August 17, 1999 A new approximate technique to solve the diffusion equation, called the Exponential Transversal Method of Lines (ETMOL), utilizes an exponential variation of the dependent variable to improve accuracy in the evaluation of the time derivative. Campo and Salazar have implemented this method in a wide range of heat/mass transfer applications and have obtained surprisingly good numerical results. In this article, we study the theoretical properties of ETMOL in depth. In particular, consistency, stability, and convergence are established within the framework of the heat/mass diffusion equation. In most practical applications, the new method presents a very reduced truncation error in time, and its different versions are proven to be unconditionally stable in the Fourier sense. Convergence of the approximate solutions have then been established. The theory is corroborated by several analytical/numerical experiments that pose different levels of complexity. c  2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 30–41, 2000 Keywords: Exponential Transversal Method of Lines (ETMOL); convergence; stability; diffusion equation; parabolic partial differential equations; numerical schemes I. INTRODUCTION This article addresses a numerical solution of the following partial differential equation (PDE): Lu ≡ ∂u ∂t − Lu = f (x,t) , for all (x,t) ∈ Q =Ω × [0, ∞) (1.1) Correspondence to: Dr. Antonio Campo, Idaho State University, College of Engineering, Campus Box 8060, Pocatello, Idaho 83209-8060 (e-mail: campanto@isu.edu) c  2000 John Wiley & Sons, Inc. CCC 0749-159X/00/010030-12