1. Sec41 The Order of Linear Multistep Methods
Given a linear multistep method [α, β], we seek conditions on the coefficients in the polynomials α and β that will guarantee that, locally, errors are O(hp+1).

2. Sec41 The Order of Linear Multistep Methods
Example: 2ed order Adams–Bashforth method

3. Sec41 The Order of Linear Multistep Methods

4. Sec41 The Order of Linear Multistep Methods

5. Sec411 Derivation of methods
Linear Multistep Methods:
find the coefficients in Adams–Moulton methods
Derivation of methods
when α is given and β is then chosen to achieve the required order

6. Sec411 Derivation of methods
Linear Multistep Methods:
find the coefficients in Adams–Bashforth methods
Derivation of methods
when α is given and β is then chosen to achieve the required order

7. Sec411 Derivation of methods
Example: 2ed order Adams–Bashforth method
find the coefficients in Adams–Bashforth methods
Derivation of methods
when α is given and β is then chosen to achieve the required order

8. Sec411 Derivation of methods
Example: 2ed order Adams–Bashforth method
First approximation
Investigate the effect of the first approximations