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).

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

Sec41 The Order of Linear Multistep Methods

Sec41 The Order of Linear Multistep Methods

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

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

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

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