NM1_basics - Why Numerical Reference Ayyub McCuen Chapter 1...

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1 Why Numerical? Reference Ayyub & McCuen Chapter 1
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2 Analytical versus Numerical Analytical closed form (exact) equation y=x 2 - 3x +2 Numerical data that represents the problem at discrete points x= 0, 1, 2, 3, 4 y= 2, 0, 0, 2, 6
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3 Analytical To write, and solve, the exact equation(s) for complex systems is difficult and many times impossible. The exact equation for the vibration of a string fixed at both ends is: ( 29 ( 29 0 x Y T dx x Y d 2 2 2 = r w +
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4 Analytical To find the derivative, integral, minimum, etc. of some functions may be very difficult. Easy: Difficult: ( 29 dx x d 2 ( 29 ( 29 ( 29 π - θ θ θ θ 4 0 1 d cos sin * tan
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5 Analytical Solving many simultaneous equations is time consuming, tedious and has many opportunities for errors.
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6 Steady-State Temperature in Flat Plate u 1 u 2 u 3 u 4 u 5 u 6 u 7 u 8 u 9 0 0 0 50 50 50 50 50 50 100 100 100
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7 The Equations 150 u 4 u u 50 u u 4 u u 50 u u 4 u 100 u u 4 u u 0 u u u 4 u u 0 u u u 4 u 150 u u 4 u 50 u u u 4 u 50 u u u 4 9 8 6 9 8 7 5 8 7 4 9 6 5 3 8 6 5 4 2 7 5 4 1 6 3
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