  A nonlinear partial differential equation is a nonlinear relationship between
an unknown function and how it changes due to two or more input variables. A
numerical method reduces such an equation to arithmetic for quick
visualization, but this can be misleading if the method is not developed and
operated carefully due to numerical oscillations, instabilities, and other
artifacts of the programmed solution. This chapter provides a friendly
introduction to error analysis of numerical methods for nonlinear partial
differential equations along with modern approaches to visually demonstrate
analytical results with confidence. These techniques are illustrated through
several detailed examples with a relevant governing equation, and lead to open
questions suggested for undergraduate-accessible research.
