Numerical methods are algorithms that produce approximate numerical solutions to mathematical problems, used when an exact analytical solution doesn’t exist or is too costly to compute.
Sources of Error
Round-Off Error
The error from representing real numbers with finite precision on a computer.
Arises because most real numbers can’t be stored exactly in a fixed number of digits, so every arithmetic operation carries a small representation error.
Truncation Error
The error from approximating an infinite or continuous process with a finite one.
Arises when a method replaces an exact mathematical operation, such as a limit, an infinite series, or a derivative, with a finite approximation.
