The Method of Lines Solution of Partial Differential Equations (Classic Reprint)

This book explains how to solve partial differential equations by first discretizing space and then integrating in time. It covers the range of spatial discretizations, how to handle boundary conditions, and how to choose stable, accurate time-stepping methods. A practical FORTRAN package named MOLID is described, guiding users to set up problems and let the software pick suitable solvers, with options to override choices when needed. The text mixes theory with concrete examples, showing how to compare approaches and judge efficiency and accuracy.

Highlights include clear guidance on keeping essential PDE properties in the discrete model, discussions of stiffness and multistep methods, and numerous numerical examples that illuminate both hyperbolic and parabolic problems. The material is accessible to scientists with limited computing experience and aims to help them solve fairly complex problems efficiently.

• Clear explanation of space discretization and boundary conditions for common PDEs


• Practical guidance on stability, convergence, and time integration


• Discussion of computational efficiency and solver choices, including iterative and Jacobian approaches


• Hands-on examples using the MOLID package to compare numerical methods

Ideal for readers of engineering and applied math who want a reliable, approachable path to solving PDEs numerically.