Numerical methods use numerical approximation rather than symbolic algebra to estimate solutions to Engineering problems to within some practical limit of uncertainty. In this context, “practical” can refer to the limits of calculational precision or to the limit of Experimental Uncertainty during a model-validating test, or to the limit of tolerance in an allocated requirement.
Most of these methods use numerical integration techniques1. Examples include Finite Element Analysis (numerically integrating across geometry), Numerical Integration (numerically integrating a definite integral having no known antiderivative), and Monte Carlo Analysis (numerically integrating through a sequence of probability density functions).
We often use these methods because we’re too lazy to find an analytic solution to a problem, even though it might require less validation.
Footnotes- Some sources consider “numerical method” and “numerical integration” to be synonymous.[↩]