Explicit two‐step Runge‐Kutta methods for computational fluid dynamics solvers
Sign Up to like & getrecommendations! Published in 2020 at "International Journal for Numerical Methods in Fluids"
DOI: 10.1002/fld.4890
Abstract: Computational fluid dynamics (CFD) has emerged as a successful tool for industry applications and basic science during the last decades. However, accurate solutions involving vortex propagation, and separated and turbulent flows, are still associated with… read more here.
Keywords: runge; runge kutta; two step; fluid dynamics ... See more keywords
Propagators for the Time-Dependent Kohn-Sham Equations: Multistep, Runge-Kutta, Exponential Runge-Kutta, and Commutator Free Magnus Methods.
Sign Up to like & getrecommendations! Published in 2018 at "Journal of chemical theory and computation"
DOI: 10.1021/acs.jctc.8b00197
Abstract: We examine various integration schemes for the time-dependent Kohn-Sham equations. Contrary to the time-dependent Schrödinger's equation, this set of equations is nonlinear, due to the dependence of the Hamiltonian on the electronic density. We discuss… read more here.
Keywords: time dependent; commutator free; runge kutta; runge ... See more keywords
Attitude Reconstruction From Inertial Measurement: Mitigating Runge Effect for Dynamic Applications
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Aerospace and Electronic Systems"
DOI: 10.1109/taes.2021.3111839
Abstract: Time-equispaced inertial measurements are practically used as inputs for motion determination. Polynomial interpolation is a common technique of recovering the gyroscope signal but is subject to a fundamentally numerical stability problem due to the Runge… read more here.
Keywords: reconstruction inertial; runge effect; runge; attitude reconstruction ... See more keywords
Round-Off Error and Exceptional Behavior Analysis of Explicit Runge-Kutta Methods
Sign Up to like & getrecommendations! Published in 2020 at "IEEE Transactions on Computers"
DOI: 10.1109/tc.2019.2917902
Abstract: Numerical integration schemes are mandatory to understand complex behaviors of dynamical systems described by ordinary differential equations. Implementation of these numerical methods involve floating-point computations and propagation of round-off errors. This paper presents a new… read more here.
Keywords: runge kutta; kutta methods; runge; round error ... See more keywords
Phase-Fitted and Amplification-Fitted Higher Order Two-Derivative Runge-Kutta Method for the Numerical Solution of Orbital and Related Periodical IVPs
Sign Up to like & getrecommendations! Published in 2017 at "Mathematical Problems in Engineering"
DOI: 10.1155/2017/1871278
Abstract: A phase-fitted and amplification-fitted two-derivative Runge-Kutta (PFAFTDRK) method of high algebraic order for the numerical solution of first-order Initial Value Problems (IVPs) which possesses oscillatory solutions is derived. We present a sixth-order four-stage two-derivative Runge-Kutta… read more here.
Keywords: order; phase fitted; method; runge ... See more keywords
Continuous-Stage Runge–Kutta Approximation to Differential Problems
Sign Up to like & getrecommendations! Published in 2022 at "Axioms"
DOI: 10.3390/axioms11050192
Abstract: In recent years, the efficient numerical solution of Hamiltonian problems has led to the definition of a class of energy-conserving Runge–Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). Such methods admit an interesting interpretation in… read more here.
Keywords: continuous stage; runge kutta; differential problems; stage runge ... See more keywords