17.1. Error Analysis in Numerical ODE Solutions

Try these first

1. 1.

   Define round-off error.

   Hint

   Consider the limitations of storing decimal values.

2. 2.

   What is local truncation error?

   Hint

   Think about the accuracy of the next computed value against the actual value.

3. 3.

   What type of error occurs due to finite precision?

   • Round-off Error
   • Truncation Error
   • Discretization Error

   Hint

   Think about how computers handle decimal points.

4. 4.

   Is the global truncation error the accumulation of local truncation errors?

   • True
   • False

   Hint

   Remember how errors stack up in processes.

5. 5.

   Given a differential equation, analyze how choosing different step sizes affects local and global truncation errors mathematically.

   Hint

   Investigate how varying h impacts your overall error across the intervals.

6. 6.

   Design a numerical method using both adaptive step size control and Richardson extrapolation. Show step-by-step how errors are managed.

   Hint

   Think creatively about the integration of both methods to enhance accuracy.