15.3. Adams–Bashforth Formulas

Try these first

1. 1.

   Write down the general formula for the k-step Adams–Bashforth method.

   Hint

   Use terms like $y$, $h$, $b$ and $f$.

2. 2.

   What is the specific formula for the 2-Step Adams–Bashforth method?

   Hint

   Remember to include the coefficients of the function evaluations.

3. 3.

   What type of method is Adams–Bashforth?

   • Explicit
   • Implicit
   • Semi-Implicit

   Hint

   Think about how the next step is calculated.

4. 4.

   The local truncation error for the k-step method is of what order?

   Hint

   Recall the relationship between steps and error order.

5. 5.

   Given an initial value problem, solve using the 3-Step Adams–Bashforth method. Determine the approximate value after four steps if initial values are provided.

   Hint

   Recall how the 3-step formula incorporates values from previous computations.

6. 6.

   Explain how the choice of step size affects the accuracy of the Adams-Bashforth methods and potential stability issues.

   Hint

   Think about the balance between speed and accuracy in numerical methods.