Locally linearized Runge-Kutta method of Dormand and Prince for large systems of initial value problems

DOI10.1016/j.jcp.2020.109946OpenAlexW3097697226MaRDI QIDQ2127009

Yanyan Li

Publication date: 19 April 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2020.109946

zbMATH Keywords

stiff systemsexponential integratorsKrylov projectionslarge scale computinglocal linearization schemes

Mathematics Subject Classification ID

Numerical analysis (65-XX) Computer science (68-XX)

Related Items

Jacobian-free high order local linearization methods for large systems of initial value problems ⋮ Computing high dimensional multiple integrals involving matrix exponentials

Uses Software

• Expokit
• Matlab
• RODAS
• ode23
• ode45
• Expint
• Algorithm 919
• Ode15s
• ode113
• ode23s
• MATLAB ODE suite
• EXPODE
• phipm
• KIOPS

Cites Work

• Unnamed Item
• Unnamed Item
• Locally linearized Runge Kutta method of Dormand and Prince
• Convergence rate of strong local linearization schemes for stochastic differential equations with additive noise
• Convergence rate of weak local linearization schemes for stochastic differential equations with additive noise
• Exponential multistep methods of Adams-type
• Chemical instabilities and sustained oscillations
• Implementation of exponential Rosenbrock-type integrators
• Jacobian-free Newton-Krylov methods: a survey of approaches and applications.
• Comparative performance of exponential, implicit, and explicit integrators for stiff systems of ODEs
• KIOPS: a fast adaptive Krylov subspace solver for exponential integrators
• Exponential Rosenbrock methods of order five -- construction, analysis and numerical comparisons
• Local linearization-Runge-Kutta methods: a class of A-stable explicit integrators for dynamical systems
• Rate of convergence of local linearization schemes for random differential equations
• Efficient integration of large stiff systems of ODEs with exponential propagation iterative (EPI) methods
• Algorithm 919
• The MATLAB ODE Suite
• Solving Ordinary Differential Equations I
• On the Form of Smooth-Front Travelling Waves in a Reaction-Diffusion Equation with Degenerate Nonlinear Diffusion
• Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
• Nineteen Dubious Ways to Compute the Exponential of a Matrix
• Expokit
• Exponential Integrators for Large Systems of Differential Equations
• New Adaptive Exponential Propagation Iterative Methods of Runge--Kutta Type
• Exponential Rosenbrock-Type Methods