📂Numerical Analysis

Numerical Analysis in Differences

Definition ¹

1. Forward Difference: $$ \begin{align*} \Delta f(x) =& f(x+h) - f(x) \\ \Delta^{r+1} f(x) =& \Delta^{r} f(x+h) - \Delta^{r} f(x) \end{align*} $$
2. Backward Difference: $$ \begin{align*} \nabla f(x) =& f(x) - f(x- h) \\ \nabla^{r+1} f(x) =& \nabla^{r} f(x) - \nabla^{r} f(x- h) \end{align*} $$

Description

Generally, the term Difference is used throughout sequences, but in numerical analysis, it specifically refers to the difference between the function values of two node points. In fact, having been seen since high school, it is a familiar operator if one is accustomed to it, but looking at frequently appearing formulas in numerical analysis, they tend to be written in quite complex manners. While it greatly aids in simplifying the representation of formulas, it is equally difficult to read.

Formulas that extensively use such operators require more algebraic manipulation than one might think, and demand a lot of practice.

See Also

• Differences in Time Series Analysis
• Finite Difference Method FDM
  • Deriving Finite Differences Using Multiple Points