15.3.1. General Formula

Try these first

1. 1.

   Define multistep methods in the context of solving ODEs.

   Hint

   Focus on how values influence predictions.

2. 2.

   What does h represent in the Adams-Bashforth formula?

   Hint

   Consider the spacing in your calculations.

3. 3.

   What does the general formula of the Adams-Bashforth method rely on?

   • Future values
   • Past values
   • Random values

   Hint

   Think about the meaning of 'predictor' in the method.

4. 4.

   The constants b_j in the Adams-Bashforth formula are derived from:

   • True
   • False

   Hint

   Focus on the weight of past evaluations.

5. 5.

   Given f(x, y) = sin(x) + y^2, calculate y(0.3) using the 4-step Adams-Bashforth method with h = 0.1, using initial values from a single-step method.

   Hint

   Watch your previous evaluations closely when applying constants!

6. 6.

   Discuss the stability of the Adams-Bashforth method compared to implicit methods. Under what conditions can the explicit method fail?

   Hint

   Reflect on how to balance accuracy with choice of step size.