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Linear Multistep Methods Analysis: Coefficients and Order Determination

Explore the order of linear multistep methods by deriving and analyzing coefficients to achieve desired accuracy locally. Investigate examples like Adams-Bashforth methods with varying coefficients to meet order requirements.

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Linear Multistep Methods Analysis: Coefficients and Order Determination

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

  3. Sec41 The Order of Linear Multistep Methods Linear Multistep Methods:

  4. Sec41 The Order of Linear Multistep Methods 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

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