Numerical Methods for Differential Algebraic Equations in Chemical Engineering

In chemical engineering, many physical processes are governed by a mix of dynamic differential equations and static algebraic constraints. Understanding how to formulate, analyze, and solve these systems is essential for accurate process simulation and control. This text-based course guides you through the fundamental theory and modern numerical techniques required to tackle these complex systems. You will transition from basic mathematical formulations to implementing robust numerical solvers for real-world chemical engineering scenarios. Along the way, you will learn how to handle index reduction, ensure consistent initial conditions, and avoid common simulation pitfalls. What you'll learn: - Understand the fundamental differences between ordinary differential equations and differential algebraic equations (DAEs). - Analyze DAE systems to determine their index and identify potential numerical challenges. - Apply consistent initialization techniques to ensure stable and accurate simulation runs. - Implement modern numerical solvers and algorithms tailored for high-index chemical process models. - Practice modeling thermodynamic equilibria and mass transfer constraints using structured algebraic equations. The course begins with foundational definitions of algebraic constraints and index classifications before moving into practical formulation strategies, step-by-step numerical methods, and realistic engineering case studies. This structured approach ensures you build a solid theoretical base before solving practical problems. This course is designed for engineering students, researchers, and practicing chemical engineers who want to strengthen their numerical modeling skills. No prior experience with advanced DAE solvers is required, though a basic understanding of calculus and introductory differential equations is recommended. Start mastering complex chemical process simulations today.