153.2. 2-Step Adams–Bashforth Method

Try these first

1. 1.

   Define the 2-Step Adams–Bashforth method in your own words.

   Hint

   Think about how past values help us calculate new ones.

2. 2.

   What is the importance of choosing an appropriate step size?

   Hint

   Consider what happens if the step size is too large.

3. 3.

   What is the primary function of the 2-Step Adams–Bashforth method?

   • To use past values to predict future values
   • Only to compute current values
   • It has no use

   Hint

   Think about what 'predicting' means in the context of this method.

4. 4.

   The formula for the 2-Step Adams-Bashforth method is based on which principle?

   • True
   • False

   Hint

   Recall how we derive numerical methods!

5. 5.

   Using the 2-Step Adams-Bashforth method, calculate $y(0.6)$ given that you have $y(0) = 1.0, y(0.2) = 1.2, f(0, 1) = 0.5, and f(0.2, 1.2) = 0.6$.

   Hint

   Ensure to apply your values correctly into the given method!

6. 6.

   Discuss the impact of a larger step size on the accuracy of the 2-Step Adams-Bashforth method.

   Hint

   Remember how numerical methods typically behave with incremental changes!