Errors

Exercises ex_1 and ex_3 summarizes the most common errors we can find in any numerical code. Here, we classified those types of errors with a brief description of each.

These errors come from the fact that: 1) space and time are discretized, 2) the information in each grid point has a fixed (and limited) number of bits (floating number), and 3) the methods can be unstable, 4) or non-conservatives.

Type of error	Description
Floating point	Any number (real, imaginary, complex, or integer) is limited to the number of bits used to define them
Roundoff error	Arithmetic among numbers in floating-point representations is not exact and is characteristic of computer hardware. Particularly in addition or subtraction, if two operands differ largely in magnitude, the smaller operand may not affect the result due to rounding limitations.
Truncation error	It is characterized by the program or algorithm which, typically, computes discrete approximations of some desired continuous quantity, e.g., discretization of the numerical domain
Stability	The methods can be unstable. In this case, the roundoff error is magnified exponentially. These are also known as amplitude errors.
Conservation	Other varieties of error are phase errors, which shift our concern to accuracy rather than stability.