The Case for Code Verification

Whilst in mechanics, for instance, structural or fluid mechanics, the governing equations can generally be written down, they are often in such a form, for example Partial Differential Equations (PDE), that closed-form solutions are only possible for simple configurations. As an undergraduate, my mathematics lecturer expressed this idea by putting a dot on an otherwise clean blackboard and then stating that if the full blackboard represented the space of known PDEs then his dot represented those that have closed-form solutions. This does not mean that exact solutions for the remaining PDEs do not exist but, simply, that they are intractable through standard mathematical manipulation.