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Unformatted text preview: y ( t ) on 0 ≤ t ≤ 1. Consider the 4 methods 1 • Method 1 y n =4 y n − 1 + 5 y n − 2 + h (4 f n − 1 + 2 f n − 2 ) • Method 2 – explicit midpoint y n = y n − 2 + 2 hf n − 1 • Method 3 – Adams Bashforth twostep y n = y n − 1 + h 2 (3 f n − 1f n − 2 ) • Method 4 – BDF twostep y n = 4 3 y n − 11 3 y n − 2 + 2 3 hf n Apply the 4 methods to the model problem using exact initial conditions, i.e., y = y (0) and y 1 = y ( h ). Use h = 0 . 01 for λ = 10, λ =10, and λ =500. Explain your results. How would reducing the stepsize h a±ect the results? Note it is recommended you implement this as a simple piece of code in, e.g., MATLAB. You need not turn in your code. Simply present the solution values you observe for the required numerical integrations in support of you explanations. 2...
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 Spring '11
 gallivan
 Numerical Analysis, Method, yn, Numerical ordinary differential equations, Linear multistep method, discretization error dn

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