Finite Difference Methods For Ordinary And Partial Differential Equations by Randall Leveque

Steady-State and Time-Dependent Problems

A concise, practical introduction to finite difference techniques for solving ordinary and partial differential equations that combines derivation of schemes with rigorous analysis of consistency, stability, and convergence; it covers elliptic, parabolic, and hyperbolic problems, discusses boundary conditions and error estimation, and compares explicit and implicit time-stepping and domain discretizations, while emphasizing implementation issues, example problems, and tools for assessing and improving numerical accuracy.