Our Consideration Has Been Centered on the Unequivocal Exponential Time Differencing (Etd) Integrators That Are Intended to Tackle Firm Semi-Straight Issues. Semi-Direct Pdes Can Be Part into a Straight Part, Which Contains the Stiffest Piece of the Elements of the Issue, and a Nonlinear Part, Which Fluctuates More Gradually Than the Straight Part. the Etd Techniques Tackle the Direct Part Precisely, and Afterward Expressly Rough the Rest of the Part By Polynomial Approximations. the Primary Part of This Venture Includes an Expository Assessment of the Strategies' Steadiness Properties So As to Introduce the Upside of These Techniques In Conquering the Soundness Limitations. Moreover, We Talk About the Numerical Challenges In Approximating the Etd Coefficients, Which Are Elements of the Direct Term of the Pde. We Address Ourselves to Depicting Different Calculations For Approximating the Coefficients, Break Down Their Exhibition and Their Computational Expense, and Gauge Their Points of Interest For an Effective Execution of the Etd Strategies.