Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
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Additive autonomous ODE partitions
Definition
Let , let be open, and let . The additive autonomous ODE partition with components and is the initial-value problem in the sense of First-order systems, initial value problems, and solutions on intervals. The term autonomous means that neither component has a separate time argument. A numerical method may evaluate explicitly and solve an equation involving implicitly; this naming convention does not assert that either exact subflow exists or that an implicit stage has a solution.
Depends on
Used by
- One-step IMEX Euler with an implicit branch and residual status Algorithm
- Conditional finite-dimensional Lie and Strang splitting residual orders Corollary
- Lie and Strang compositions of exact split flows Definition
- The ARS(2,2,2) additive tableau and its three stages Definition
- An explicitly treated stiff decay mode is unstable for a large step Example
- IMEX Euler is first-order convergent on a common compact tube Theorem
- Lie and Strang splitting have global orders one and two, with separate subflow errors Theorem
Dependency tree · two levels
3 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Uri M. Ascher, Steven J. Ruuth, and Raymond J. Spiteri, Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations (standard reference, not scraped)
- Lorenzo Pareschi and Giovanni Russo, Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation (standard reference, not scraped)