A block Krylov subspace time-exact solution method for linear ordinary differential equation systems

DOI10.1002/nla.1865zbMath1313.65181OpenAlexW2101186087WikidataQ115405345 ScholiaQ115405345MaRDI QIDQ2931523

Mikhail A. Botchev

Publication date: 25 November 2014

Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nla.1865

zbMATH Keywords

algorithmswave equationnumerical examplesMaxwell's equationsmethod of linestruncated singular value decompositionmatrix exponentialblock Krylov subspace methodsexponential time integrationconvection diffusion problem

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Wave equation (35L05) Iterative numerical methods for linear systems (65F10) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Maxwell equations (35Q61) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items (13)

Exponential Krylov time integration for modeling multi-frequency optical response with monochromatic sources ⋮ A block Krylov subspace implementation of the time-parallel Paraexp method and its extension for nonlinear partial differential equations ⋮ A posteriorierror estimators for linear reduced-order models using Krylov-based integrators ⋮ APPROXIMATION OF THE LINEAR COMBINATION OF <i>φ</i>-FUNCTIONS USING THE BLOCK SHIFT-AND-INVERT KRYLOV SUBSPACE METHOD ⋮ Improved numerical solution of multi-asset option pricing problem: a localized RBF-FD approach ⋮ A scalable exponential-DG approach for nonlinear conservation laws: with application to Burger and Euler equations ⋮ An Exponential Time Integrator for the Incompressible Navier--Stokes Equation ⋮ Block Krylov subspace methods for approximating the linear combination of \(\varphi\)-functions arising in exponential integrators ⋮ KIOPS: a fast adaptive Krylov subspace solver for exponential integrators ⋮ Iterative across-time solution of linear differential equations: Krylov subspace versus waveform relaxation ⋮ ART: adaptive residual-time restarting for Krylov subspace matrix exponential evaluations ⋮ Krylov subspace exponential time domain solution of Maxwell's equations in photonic crystal modeling ⋮ Exponential Time Integrators for Unsteady Advection–Diffusion Problems on Refined Meshes

Uses Software

• Expokit
• Matlab
• UMFPACK
• Expint
• Algorithm 919
• ddesd
• VAC

Cites Work

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