Finite Difference Methods for Ordinary and Partial Differential Equations

Finite Difference Methods for Ordinary and Partial Differential Equations introduces the fundamental techniques used in approximating solutions to both ODEs and PDEs. The book carefully examines the similarities and differences in algorithm design and stability analysis, presenting a unified perspective on stability theory that bridges the gap between ordinary and partial differential equations. Structured into two main parts and several appendices, the text begins with steady-state boundary value problems in Part I. It starts with two-point boundary value problems in one dimension and progresses to elliptic problems in two and three dimensions, culminating with a discussion on iterative methods for large sparse linear systems arising from difference approximations. Part II shifts focus to time-dependent problems. It opens with the initial value problem for ODEs and advances to initial boundary value problems for parabolic and hyperbolic PDEs before exploring mixed equations that merge features from each of these classes. The appendices consolidate essential concepts relevant to both sections, enriching the reader’s understanding. With exercises, student projects, and a wealth of MATLAB m-files provided as supplementary material, this book offers a solid foundation in the development, analysis, and practical application of finite difference methods, preparing students to tackle more complex topics in the field.