What does 'discretization' mean in computational methods?

Discretization refers to the process of transforming continuous functions into discrete counterparts, which is essential in computational methods. In many engineering and scientific applications, problems are modeled using continuous mathematics (e.g., differential equations). However, computers operate using discrete data. Therefore, discretization is necessary to perform numerical simulations and analyses.

This process typically involves dividing a continuous domain into a finite number of small segments or elements, allowing for numerical approximation methods to be applied. By doing so, integrals, derivatives, and other continuous operations can be approximated using algebraic equations. This approach underpins many numerical techniques, such as finite difference methods or finite element methods, which are widely used in engineering analysis.

The other options pertain to different concepts in computational methods but do not encapsulate discretization's fundamental meaning. For instance, solving linear equations is a direct outcome of using discretized data, but it does not define the process of discretization itself. Similarly, maximizing output deals with optimization rather than the transition from continuous to discrete models, and linearizing nonlinear systems pertains to simplifying equations rather than discretization.