Numerical Methods for Chemical Engineering: Solving Boundary Value Problems

Chemical engineering systems rely heavily on transport phenomena, reaction kinetics, and diffusion processes that are mathematically described by boundary value problems. This text-based course bridges the gap between theoretical chemical engineering principles and the practical numerical techniques needed to solve these complex differential equations. You will learn to translate physical conservation laws into robust computational models that simulate real-world chemical processes. By working through structured written explanations and step-by-step mathematical derivations, you will gain the confidence to set up, discretize, and solve boundary value problems. You will explore modern computational workflows, including error analysis and stability checks, to ensure your simulations are both accurate and efficient. What you'll learn: - Understand the fundamental classification of boundary value problems in chemical engineering processes - Apply the finite difference method to discretize ordinary and partial differential equations - Solve non-linear boundary value problems using iterative numerical solvers - Configure appropriate boundary conditions, including Dirichlet, Neumann, and Robin types, for physical accuracy - Implement error estimation and grid convergence studies to validate your numerical solutions - Practice translating physical transport phenomena into structured, solvable mathematical models This course begins with essential definitions, scaling analysis, and foundational mathematical concepts before guiding you through discretization techniques and iterative solvers. You will read comprehensive explanations, study practical code representations, and work through analytical exercises designed to solidify your engineering intuition. This course is designed for undergraduate chemical engineering students, computational science beginners, and practicing engineers looking to refresh their numerical modeling skills. No prior experience with advanced numerical solvers is required, though a basic understanding of calculus and introductory chemical engineering concepts is recommended. Start reading today to master the numerical methods that power modern chemical process simulation.