BAMPHI: matrix-free and transpose-free action of linear combinations of \(\varphi\)-functions from exponential integrators

DOI10.1016/j.cam.2022.114973zbMath1503.65142OpenAlexW4310209557MaRDI QIDQ2112711

Franco Zivcovich, Fabio Cassini, Marco Caliari

Publication date: 11 January 2023

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2022.114973

zbMATH Keywords

backward error analysisstiff ODEsmatrix exponentialexponential integratorslinear combinations of \(\varphi\)-functions

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for stiff equations (65L04) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items (3)

Efficient inversion of matrix \(\varphi \)-functions of low order ⋮ Accelerating Exponential Integrators to Efficiently Solve Semilinear Advection-Diffusion-Reaction Equations ⋮ A second order directional split exponential integrator for systems of advection-diffusion-reaction equations

Uses Software

• Algorithm 919
• phipm

Cites Work

• Unnamed Item
• On the preservation of phase space structure under multisymplectic discretization
• Implementation of exponential Rosenbrock-type integrators
• Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices
• A study of extrapolation methods based on multistep schemes without parasitic solutions
• On-the-fly backward error estimate for matrix exponential approximation by Taylor algorithm
• Backward error analysis of polynomial approximations for computing the action of the matrix exponential
• Low regularity exponential-type integrators for semilinear Schrödinger equations
• A comparison of boundary correction methods for Strang splitting
• On hybrid iterative methods for nonsymmetric systems of linear equations
• KIOPS: a fast adaptive Krylov subspace solver for exponential integrators
• Efficient exponential Runge-Kutta methods of high order: construction and implementation
• An accurate and time-parallel rational exponential integrator for hyperbolic and oscillatory PDEs
• A \(\mu\)-mode integrator for solving evolution equations in Kronecker form
• Approximation of the matrix exponential for matrices with a skinny field of values
• Further development of efficient and accurate time integration schemes for meteorological models
• A massively parallel exponential integrator for advection-diffusion models
• Efficient integration of large stiff systems of ODEs with exponential propagation iterative (EPI) methods
• The Leja Method Revisited: Backward Error Analysis for the Matrix Exponential
• Exponential integrators
• Algorithm 919
• Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators
• Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
• On Magnus Integrators for Time-Dependent Schrödinger Equations
• Stochastic exponential integrators for the finite element discretization of SPDEs for multiplicative and additive noise
• A General Framework of Low Regularity Integrators
• Exponential Rosenbrock-Type Methods
• Fourth-Order Time-Stepping for Stiff PDEs
• The Numerical Range is a $(1+\sqrt{2})$-Spectral Set
• Geometric Numerical Integration

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