Explicit and implicit time integration techniques are frequently required in numerical approaches. Explicit schemes are constrained by stringent stability requirements, yet they are straightforward and affordable per time step. Conversely, implicit techniques allow for considerably bigger time steps but also increase computational costs by requiring the solution of complex systems at each iteration. Thus, objective of developing more efficient time methods for stiff systems is to provide alternative methods which have better stability properties than explicit schemes and require fewer arithmetic operations per time step than implicit methods. In this work, we develop ETD methods efficiently, which handle stiffness by treating linear and nonlinear terms separately, allowing larger time steps without losing accuracy, that preserve key physical properties, such as energy dissipation and stability. Numerical experiments demonstrate that the proposed methods achieve high accuracy and robustness, even for long-time simulations. Acknowledgment: The author acknowledge the financial support of the Deanship of Research at King Fahd University of Petroleum and Minerals (KFUPM), Saudi Arabia, through project # CONF2600, in accomplishing this work.