A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides
From MaRDI portal
Publication:4371743
DOI10.1145/79505.79507zbMath0900.65234OpenAlexW2139482396MaRDI QIDQ4371743
Publication date: 9 February 1998
Published in: ACM Transactions on Mathematical Software (Search for Journal in Brave)
Full work available at URL: http://www.acm.org/pubs/contents/journals/toms/1990-16/
Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)
Related Items
Computer-algebra multiple-timescale method for spatially periodic thin-film viscous-flow problems ⋮ A modified approach to wavemaker modeling for high-order spectral numerical wave tanks ⋮ Genetic demographic networks: mathematical model and applications ⋮ A simple, optimally convergent, parameter-free discretization of diffusive terms with the discontinuous Galerkin method ⋮ An analytical solution of the isentropic vortex problem in the special relativistic magnetohydrodynamics ⋮ On the efficiency of 5(4) RK-embedded pairs with high order compact scheme and Robin boundary condition for options valuation ⋮ A new mesh selection strategy with stiffness detection for explicit Runge-Kutta methods ⋮ An efficient and uniformly behaving streamline-based \(\mu\)CT fibre tracking algorithm using volume-wise structure tensor and signal processing techniques ⋮ Nonlinear model updating through a hierarchical Bayesian modeling framework ⋮ Diffraction and interference with run-and-tumble particles ⋮ Computer-aided experiments on the Hopf bifurcation of the FitzHugh-Nagumo nerve model ⋮ On explicit two-derivative Runge-Kutta methods ⋮ Numerical schemes for solving and optimizing multiscale models with age of hepatitis C virus dynamics ⋮ Nonlinear higher-order spectral solution for a two-dimensional moving load on ice ⋮ Hamiltonian dynamics and control of a joint autonomous land-air operation ⋮ Semi-Numerical, Semi-Analytical Approximations of the Rayleigh Equation for Gas-Filled Hyper-Spherical Bubble ⋮ Support vector classifiers via gradient systems with discontinuous righthand sides ⋮ Direct dynamical energy cascade in the modified KdV equation ⋮ Accelerating moderately stiff chemical kinetics in reactive-flow simulations using GPUs ⋮ Solving large-deflection problem of spatial beam with circular cross-section using an optimization-based Runge-Kutta method ⋮ Bubble dynamics in a Maxwell fluid with extensional viscosity ⋮ Numerical simulation of thin paint film flow ⋮ Generalizing global error estimation for ordinary differential equations by using coupled time-stepping methods ⋮ Diffusion transitions in a 2D periodic lattice ⋮ HOS-ocean: open-source solver for nonlinear waves in open ocean based on high-order spectral method ⋮ Acceleration of supersonic/hypersonic reactive CFD simulations via heterogeneous CPU-GPU Supercomputing ⋮ Chaotic contact dynamics of two microbeams under various kinematic hypotheses ⋮ Efficient solution of bimaterial Riemann problems for compressible multi-material flow simulations ⋮ Error control of the numerical posterior with Bayes factors in Bayesian uncertainty quantification ⋮ Eulerian-Lagrangian method for simulation of cloud cavitation ⋮ A modified high-order spectral method for wavemaker modeling in a numerical wave tank ⋮ A New Class of High-Order Methods for Multirate Differential Equations ⋮ Probabilistic solvers enable a straight-forward exploration of numerical uncertainty in neuroscience models ⋮ High order methods for the integration of the Bateman equations and other problems of the form of \(y^{\prime}=F(y,t)y\) ⋮ Nonlinear motion of an oscillating bubble immersed in a magnetic fluid ⋮ A test set for stiff initial value problem solvers in the open source software R: Package \textbf{deTestSet} ⋮ Bubble cloud dynamics in an ultrasound field ⋮ Efficient path tracking methods ⋮ Local error estimation and step size control in adaptive linear multistep methods ⋮ The compact gradient recovery discontinuous Galerkin method for diffusion problems ⋮ Stochastic kinetics of the circular gene hypothesis: feedback effects and protein fluctuations ⋮ Periodic orbits for the perturbed planar circular restricted 3-body problem ⋮ An adaptive and explicit fourth order Runge-Kutta-Fehlberg method coupled with compact finite differencing for pricing American put options ⋮ On the interaction of vortices with mixing layers ⋮ Linear stability of a Berman flow in a channel partially filled with a porous medium ⋮ Fast and efficient chemical process flowsheet simulation by pseudo-transient continuation on inertial manifolds ⋮ An accelerated iterative method for the dynamics of constrained multibody systems ⋮ A numerical study of a detonation wave in detonation transmission tubing ⋮ Multidomain Galerkin–collocation method: spherical collapse of scalar fields II ⋮ Optimising code generation with haggies ⋮ TSIL: a program for the calculation of two-loop self-energy integrals ⋮ Using a template engine as a computer algebra tool ⋮ A time finite element method for structural dynamics ⋮ Finite-volume WENO scheme for viscous compressible multicomponent flows ⋮ Unsteady motion of a spherical bubble in a complex fluid: mathematical modelling and simulation ⋮ Nonlinear dynamics of a bubble contrast agent oscillating near an elastic wall ⋮ Implementation of an elastic–viscoplastic ductile model for the numerical simulation of the ductile crack growth in notched tensile and Charpy impact tests ⋮ An OpenCL implementation for the solution of the time-dependent Schrödinger equation on GPUs and CPUs ⋮ Modulational instability of co-propagating internal wavetrains under rotation ⋮ Multidomain Galerkin-collocation method: characteristic spherical collapse of scalar fields ⋮ A boundary integral method with volume-changing objects for ultrasound-triggered margination of microbubbles ⋮ Comparing epidemiological models with the help of visualization dashboards ⋮ Hyperchaos and multistability in the model of two interacting microbubble contrast agents ⋮ Positivity-preserving adaptive Runge-Kutta methods ⋮ A Gauss-Seidel projection method with the minimal number of updates for the stray field in micromagnetics simulations ⋮ Embedded (4, 5) pairs of explicit 7-stage Runge-Kutta methods with FSAL property ⋮ Bubbling transition as a mechanism of destruction of synchronous oscillations of identical microbubble contrast agents ⋮ Numerical methods, energy conservation, and a new method for particle motion in magnetic fields ⋮ Automatic differentiation of numerical integration algorithms ⋮ CRPropa 3.1—a low energy extension based on stochastic differential equations ⋮ Mathematical modeling of nonlinear thermodynamics of nanoplates ⋮ Adaptive methods for stochastic differential equations via natural embeddings and rejection sampling with memory