Solutions of the Cahn–Hilliard EquationsSecond Revised and Expanded Editionby Rahul Basu

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 principles
•Matrix formulations and coupled second-order systems
•Finite-difference, spectral, and finite-element methods
•Sparse-matrix techniques and the Conjugate Gradient method
•Stability analysis and modern time-integration schemes
•Complete, ready-to-run programs in MATLAB, Python (NumPy/SciPy), and Wolfram Language
•Phase-field modelling and industrial applications (batteries, additive manufacturing, polymer blends, etc.)
•Benchmark problems, validation cases, and exercises

Written 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.