Math 294-0138
D. Prapavessi, Fall 2009
Worksheet 12
Consider the IVP 
(*).
A. Solve the initial value problem above algebraically.
B.
Use Euler’s method and the improved Euler’s method to approximate the
solution on the interval 
with
step size h = 0.2 and 0.005
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x |
Euler’s h=0.2 |
Euler’s h=0.005 |
Improved Euler’s f(x) |
Improved Euler’s f(x) |
Actual f(x) |
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2 |
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2.2 |
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2.4 |
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2.6 |
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2.8 |
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3.0 |
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C. Use Euler’s method to approximate the solution to (*) at x =3 with step size h = 0.1 and 0.05, 0.025, 0.0125, .00625 – each time calculate the error and the quantity |Error|/h. What do you conclude?
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h |
f(1) |
error |
|error|/h |
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0.1 |
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0.05 |
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0.025 |
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0.0125 |
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0.00625 |
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D. Use the improved Euler’s method to approximate the solution to (*) at x =3 with step size h = 0.1 and 0.05, 0.025, 0.0125, .00625 – each time calculate the error and the quantity |Error|/h. What do you comclude?
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h |
f(1) |
error |
|error|/h2 |
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0.1 |
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0.05 |
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0.025 |
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0.0125 |
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0.00625 |
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