ABSTRACT
This chapter presents the successful study of approximate solution techniques that requires knowledge of physics, mathematics and some rudimentary aspects of computer science. Analysts are routinely called upon to numerically simulate physical phenomena of varying complexity. To successfully perform such simulations, the phenomena must first be described mathematically. Such descriptions consist of the equations governing the phenomena and suitable boundary conditions, initial conditions, or both, that, are imposed on the governing equations. The mathematical description is typically referred to as the classical or strong form of a problem. However, in many real-world applications the complexity of problems precludes their solution exactly. Instead, such problems must be solved using approximate techniques. When developing such techniques the diversity of the aforementioned physical problems represents a potential source of confusion, for it may not always be clear whether a particular technique is general in nature or is applicable only to a given class of problems.
