ABSTRACT
Understanding error is fundamental to any numerical analysis and thus important for CNDE. CNDE requires numerical methods that need to be stable and converged. Sometimes, the computational burden is so high that algorithm has no choice except sacrificing the accuracy. However, that is not desired. Hence, advance computing platform is necessary. Every numerical method has its own requirements for convergence and specially, CNDE requires heavy computation with better computing architecture. In this chapter, thus basic understanding of error, error propagation, convergence, and stability of algorithms are discussed. Taylor series expansion, which is fundamental to most numerical technique, is introduced and step by step finite different method is introduced. Most of the CNDE problem as simulate wave propagation belongs to the dynamic system. Basic solution methodologies for any dynamic system derived from finite difference method are presented and their respective use is commented. As CNDE could be heavy with its computational burden, it requires parallel computing architecture. Thus, basic understanding of parallel the computing is described in this chapter for the reader to follow the respective discussions in respective chapters on the parallel computing enabled CNDE methods.
