ABSTRACT
Part 4 describes how to find numerical solutions to differential equations. Sometimes numerical solutions are created when exact or approximate solutions cannot be obtained. Other times, a numerical solution may be more useful. First, there are 10 sections with useful overall information for numerical solutions of differential equations (“How to determine a computational grid?” and “How to assess if a method is stable”). Then, there are almost 40 section on different numerical techniques; these are separated into techniques for ordinary and partial differential equation. The familiar techniques appear (“Euler's method”) as well as topics useful for precise computation (such as symplectic integration). Methods are included that apply specifically to parabolic, hyperbolic, and elliptic partial differential equations.
