17.. Numerical Solutions of ODEs

Try these first

1. 1.

   What is round-off error?

   Hint

   Think about how numbers are stored in computers.

2. 2.

   Define local truncation error.

   Hint

   Refer to how errors accumulate over steps.

3. 3.

   What type of error is caused by the limited precision of computer arithmetic?

   • Round-off Error
   • Truncation Error
   • Discretization Error

   Hint

   Think about how computers handle digits.

4. 4.

   The global truncation error accumulates over how many integration steps?

   Hint

   Consider what happens to errors when you perform multiple steps.

5. 5.

   Assume you have implemented Euler's method for a function. Describe how you would analyze the local truncation error in your implementation.

   Hint

   Remember to refer to the formula for local truncation error.

6. 6.

   Given a numerical method with a known global truncation error of O(h^3), can you reason out the implications for the accuracy of the method if the step size is halved?

   Hint

   Consider the relationship between step size and the error term.