For many applied engineering problems, we cannot obtain analytical solutions. Therefore, we cannot compute exactly the errors associated with our numerical methods. In these case, we must settle for approximations or estimates of the errors.
Such errors are characteristic of most of the techniques. In professional practice, errors can be costly and sometimes catastrophic. If a structure or device fails, lives can be lost. On of the two major forms of numerical error: round-off error and truncation error.
Round-off error
Is due to the fact that computers can represent only quantities with a finite number of digits.
Truncation Error
Is the discrepancy introduced by the fact that numerical methods may employ approximations to represent exact mathematical operations and quatities.
