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mws_gen_aae_spe_sourcesoferror - Chapter 01.03 Sources of...

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01.03.1 Chapter 01.03 Sources of Error After reading this chapter, you should be able to: 1. know that there are two inherent sources of error in numerical methods – round- off and truncation error, 2. recognize the sources of round-off and truncation error, and 3. know the difference between round-off and truncation error. Error in solving an engineering or science problem can arise due to several factors. First, the error may be in the modeling technique. A mathematical model may be based on using assumptions that are not acceptable. For example, one may assume that the drag force on a car is proportional to the velocity of the car, but actually it is proportional to the square of the velocity of the car. This itself can create huge errors in determining the performance of the car, no matter how accurate the numerical methods you may use are. Second, errors may arise from mistakes in programs themselves or in the measurement of physical quantities. But, in applications of numerical methods itself, the two errors we need to focus on are 1. Round off error 2. Truncation error. Q : What is round off error? A : A computer can only represent a number approximately. For example, a number like 3 1 may be represented as 0.333333 on a PC. Then the round off error in this case is 3 0000003 . 0 333333 . 0 3 1 . Then there are other numbers that cannot be represented exactly. For example, and 2 are numbers that need to be approximated in computer calculations. Q : What problems can be created by round off errors? A : Twenty-eight Americans were killed on February 25, 1991. An Iraqi Scud hit the Army barracks in Dhahran, Saudi Arabia. The patriot defense system had failed to track and intercept the Scud. What was the cause for this failure? The Patriot defense system consists of an electronic detection device called the range gate. It calculates the area in the air space where it should look for a Scud. To find out where it
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01.03.2 Chapter 01.03
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