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Differential Equations

Differential Equations

Accuracy and Usefulness of Euler's Method Exercises

Example 1

Let y = f (x) be a solution to the IVP

What is the error when Euler's method is used to estimate f (2) with a step size of 0.5? With a step size of 0.25?

Example 2

If f is concave up around x = a, is the tangent line to f at a above or below the graph of f? What about if f is concave down?

Example 3

Let y = f (x) be a solution to the IVP

Does Euler's method produce an over- or under-estimate for the value of f (2)?

Example 4

Let y = f (x) be a solution to the IVP

Does Euler's method produce an over- or under-estimate for the value of f (3.5)?

Example 5

Let y = f (x) be a solution to the IVP

Does Euler's method produce an over- or under-estimate for the value of f (1)?

Example 6

Let y = f (x) be a solution to the IVP

Does Euler's method produce an over- or under-estimate for the value of f (2)?

Example 7

Let y = f (x) be a solution to the IVP

Does Euler's method produce an over- or under-estimate for the value of f (5.9)?

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