EAD 115

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EAD 115

• Numerical Solution of Engineering and Scientific
  Problems
• David M. Rocke
• Department of Applied Science

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Why Study Numerical Methods?

• Solution of engineering and scientific problems
  can be done by theory or experiment
• An important third way is by computation
• We would rather have an approximate answer to the
  right problem than an exact answer to the wrong
  problem (consider a spherical cow)

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Mathematical Models

• If we can describe a problem via a mathematical
  model, we can often find out much about the real
  problem by studying the mathematical model
• Simple mathematical models can be solved with
  pencil and paper
• Realistic models usually require computer solution

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The parachutist

• Downward force due to gravity
• Upward force due to air resistance

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Analytical vs. Numerical Solutions

• The previous solution is analytical, meaning that
  it is supplied by a single simple formula
• We can solve this problem also numerically
• Numerical solutions generalize
• What if the drag is not linear in the velocity?

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Eulers Method