6533b7ddfe1ef96bd12751e0
RESEARCH PRODUCT
High-order Runge–Kutta–Nyström geometric methods with processing
Sergio BlanesJosé Luis Regidor RosFernando Casassubject
Numerical AnalysisDifferential equationApplied MathematicsMathematical analysisMathematicsofComputing_NUMERICALANALYSISLie groupMathematics::Numerical AnalysisComputational MathematicsRunge–Kutta methodsKernel methodKernel (image processing)Ordinary differential equationLie algebraInitial value problemApplied mathematicsMathematicsdescription
Abstract We present new families of sixth- and eighth-order Runge–Kutta–Nystrom geometric integrators with processing for ordinary differential equations. Both the processor and the kernel are composed of explicitly computable flows associated with non trivial elements belonging to the Lie algebra involved in the problem. Their efficiency is found to be superior to other previously known algorithms of equivalent order, in some case up to four orders of magnitude.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2001-12-01 | Applied Numerical Mathematics |