trinstørrelse

Trinstørrelse, or step size, is the size of the increment between successive points in a discretized representation of a continuous quantity. It is a central concept in numerical methods, data processing and experimental design, where a continuous phenomenon is modeled, measured or simulated by a finite set of points.

In numerical analysis, the step size is the interval h used to advance solutions in time or along a spatial grid. The choice of trinstørrelse affects accuracy and computational effort: smaller steps generally increase accuracy but require more computations, while larger steps reduce cost but can introduce larger truncation or round-off errors. For many methods, the global error scales with a power of h (for example, O(h) for first-order methods, O(h^p) for p-th order methods). Stability considerations often constrain how large the step size can be, especially for time-dependent problems. For partial differential equations, conditions such as the CFL (Courant–Friedrichs–Lewy) criterion relate the time step to the spatial step and characteristic speeds to ensure stable solutions.

Outside numerical simulation, trinstørrelse also appears in data processing and measurement. The step size can refer to the sampling interval or bin width in histograms and signal processing, influencing resolution, aliasing and noise sensitivity. In experimental planning, the step size helps determine the density of measurements needed to capture variation without excessive effort.

Terminology varies across languages, but the concept remains the same: step size is the discrete spacing between consecutive points in a representation of a continuous quantity. Adaptive step-size methods dynamically adjust h to balance accuracy and efficiency.