Solutions of the Cahn-Hilliard Equations--Second Revised and Expanded Edition

Solutions of the Cahn-Hilliard Equations---Second Revised and Expanded Edition The Cahn-Hilliard equation is one of the most important nonlinear partial differential equations in modern materials science. It describes phase separation, spinodal decomposition, and microstructure evolution in binary alloys, polymers, batteries, thin films, and many other systems.This second revised and expanded edition provides a complete, practical guide to solving the equation analytically and numerically. Unlike purely theoretical texts, the book integrates rigorous mathematical derivations with fully working computer implementations.What you will find inside:Clear derivation of the Cahn-Hilliard equation from free-energy principlesMatrix formulations and coupled second-order systemsFinite-difference, spectral, and finite-element methodsSparse-matrix techniques and the Conjugate Gradient methodStability analysis and modern time-integration schemesComplete, ready-to-run programs in MATLAB, Python (NumPy/SciPy), and Wolfram LanguagePhase-field modelling and industrial applications (batteries, additive manufacturing, polymer blends, etc.)Benchmark problems, validation cases, and exercisesWritten for postgraduate students, researchers, and practising engineers in computational materials science, applied mathematics, and numerical analysis, this volume serves both as a textbook and a practical reference.All numerical examples can be reproduced directly from the codes provided. Whether you are learning the theory or implementing large-scale phase-field simulations, this book offers a unified and hands-on approach to the Cahn-Hilliard equation.