Chapter 4 Linear Multistep Methods Example 2 ed

Chapter 4: Linear Multistep Methods Example: 2 ed order backward difference formula (BDF 2) Example: 2 ed order Adams–Bashforth method Example: 3 ed order Adams–Bashforth method Linear Multistep Methods:

Chapter 4: Linear Multistep Methods: Two Polynomials we write the method as [α, β], where Other textbook )ρ, σ, ( Example: (BDF 2) Example: 2 ed order Adams–Bashforth method

Chapter 4: Linear Multistep Methods: Starting methods linear multistep methods require starting methods even to carry out a single step. One obvious approach to starting a k-step method is to carry out k − 1 steps with a Runge–Kutta method, preferably of the same order as the linear multistep method itself. Example: 2 ed order Adams–Bashforth method given approximate

Sec 404: Consistency Linear Multistep Methods: Example: (BDF 2) Definition 404 A A linear multistep method satisfying is said to be ‘preconsistent’ Example: 2 ed order Adams–Bashforth method

Sec 404: Consistency Linear Multistep Methods: Definition 404 A A linear multistep method satisfying is said to be ‘consistent’ Example: (BDF 2) Example: 2 ed order Adams–Bashforth method

Sec 404: Consistency Linear Multistep Methods:

Sec 403: Stability Linear Multistep Methods: Definition 403 A A linear multistep method [α, β] is ‘stable’ if the difference equation has only bounded solutions. all solutions are bounded if and only if the polynomial has all its zeros in the closed unit disc and all multiple zeros in the interior of this disc.

Sec 403: Stability Linear Multistep Methods: Definition 403 A A linear multistep method [α, β] is ‘stable’ if the difference equation has only bounded solutions. Example: 2 ed order Adams–Bashforth method all solutions are bounded if and only if the polynomial has all its zeros in the closed unit disc and all multiple zeros in the interior of this disc. Example: (BDF 2)

Sec 403: Stability Linear Multistep Methods: Definition 402 A

Sec 403: Stability Linear Multistep Methods: Theorem

Sec 403: Stability Linear Multistep Methods: Definition Example: 2 ed order Adams–Bashforth method

Sec 403: Stability Linear Multistep Methods: Definition