Higher-order additive Runge–Kutta schemes for ordinary differential equations

Kennedy, Christopher; Carpenter, Mark H.

doi:10.1016/j.apnum.2018.10.007

Cited by 53 publications

(31 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the present study, the strength of predictor-corrector Adams technique [22,23] and explicit Runge-Kutta numerical technique [24,25] is exploited to solve the second-order prediction differential model.…”

Section: Methodsmentioning

confidence: 99%

Design of a Novel Second-Order Prediction Differential Model Solved by Using Adams and Explicit Runge–Kutta Numerical Methods

Sabir

Guirao

Saeed

et al. 2020

Mathematical Problems in Engineering

View full text Add to dashboard Cite

In this study, a novel second-order prediction differential model is designed, and numerical solutions of this novel model are presented using the integrated strength of the Adams and explicit Runge–Kutta schemes. The idea of the present study comes to the mind to see the importance of delay differential equations. For verification of the novel designed model, four different examples of the designed model are numerically solved by applying the Adams and explicit Runge–Kutta schemes. These obtained numerical results have been compared with the exact solutions of each example that indicate the performance and exactness of the designed model. Moreover, the results of the designed model have been presented numerically and graphically.

show abstract

Section: Methodsmentioning

confidence: 99%

Design of a Novel Second-Order Prediction Differential Model Solved by Using Adams and Explicit Runge–Kutta Numerical Methods

Sabir

Guirao

Saeed

et al. 2020

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“… Note . (ARS: Ascher et al, , BRS: Boscarino et al, , CGG: Conde et al, , GU: Guerra & Ullrich, , KC03: Kennedy & Carpenter, , KC19: Kennedy & Carpenter , RMC: Rokhzadi et al, , SVTG: Steyer et al, , * fully explicit ).…”

Section: Methodsmentioning

confidence: 99%

Evaluation of Implicit‐Explicit Additive Runge‐Kutta Integrators for the HOMME‐NH Dynamical Core

Vogl

Steyer

Reynolds

et al. 2019

J Adv Model Earth Syst

View full text Add to dashboard Cite

The nonhydrostatic High-Order Method Modeling Environment (HOMME-NH) atmospheric dynamical core supports acoustic waves that propagate significantly faster than the advective wind speed, thus greatly limiting the time step size that can be used with standard explicit time integration methods. Resolving acoustic waves is unnecessary for accurate climate and weather prediction. This numerical stiffness is addressed herein by considering implicit-explicit additive Runge-Kutta (ARK IMEX) methods that can treat the acoustic waves in a stable manner without requiring implicit treatment of nonstiff modes. Various ARK IMEX methods are evaluated for their efficiency in producing accurate solutions, ability to take large time step sizes, and sensitivity to grid cell length ratio. Both the gravity wave test and baroclinic instability test from the 2012 Dynamical Core Model Intercomparison Project are used to recommend 5 of the 27 ARK IMEX methods tested for use in HOMME-NH. (E3SM) is an ongoing effort to produce actionable projections of variability and change in the Earth system. Advances in computational power have allowed endeavors like E3SM to simulate physical phenomena at finer resolution than ever before. Modeling the atmosphere at these finer resolutions requires improving both the underlying mathematical models and computational techniques. This works focuses on the latter by evaluating cutting-edge computational techniques on a recently developed atmosphere model and suggesting which of those techniques should be included in the next generation of E3SM. Plain Language Summary The Energy Exascale Earth System Model

show abstract

“…[25] and IMEX-DIM-SIM3 from [14]. At order 4, comparisons are done against ARK4(3)7L[2]SA 1 from [26] and IMEX-DIMSIM4 from [35]. Order 5 serial methods are ARK5(4)8L[2]SA 2 from [26] and IMEX-DIMSIM5 from [35].…”

Section: Allen-cahn Problemmentioning

confidence: 99%

“…At order 4, comparisons are done against ARK4(3)7L[2]SA 1 from [26] and IMEX-DIMSIM4 from [35]. Order 5 serial methods are ARK5(4)8L[2]SA 2 from [26] and IMEX-DIMSIM5 from [35]. Finally, the order 6 baseline is IMEX-DIMSIM6(S ∕2 ) from [24].…”

Section: Allen-cahn Problemmentioning

confidence: 99%