Euler's Method and Backwards Euler 

It's always a good idea to begin your page with a "restart" command -- so when re-running 

commands, you can start with a blank slate. 

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I will use our example equation from class. 

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Maple easily solves our initial value problem. 

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Let's approximate using a step size of . This means we need iterations. 

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Here's Euler's Method. 

and (from our initial condition) 

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Our approximation of is . I let's print out a decimal approximation of . 

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The exact value of is given below: 

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The difference between the exact value and the approximated value gives us the "global truncation error". 

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Here's Backwards Euler's Method. 

Recall the Backwards Euler's is an implicit method. So we need to solve 

for each time through the loop. 

and (from our initial condition) 

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Our approximation of is . I let's print out a decimal approximation of . 

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The exact value of is given below: 

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The difference between the exact value and the approximated value gives us the "global truncation error". 

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