On convergence of waveform relaxation for nonlinear systems of ordinary differential equations
DOI10.1007/s10092-024-00578-0zbMATH Open1542.65073MaRDI QIDQ6566103
Publication date: 3 July 2024
Published in: Calcolo (Search for Journal in Brave)
Burgers equationKrylov subspaceswaveform relaxationnonlinear heat conduction equationLiouville-Bratu-Gelfand equationexponential time integratorstime-parallel methods
Stability and convergence of numerical methods for ordinary differential equations (65L20) Parallel numerical computation (65Y05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical computation of matrix exponential and similar matrix functions (65F60)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The Liouville-Bratu-Gelfand problem for radial operators
- RKC time-stepping for advection-diffusion-reaction problems
- High-order splitting schemes for semilinear evolution equations
- Weighted sequential splittings and their analysis
- Choice of initial guess in iterative solution of series of systems arising in fluid flow simulations
- An iterative solution method for solving \(f(A)x=b\), using Krylov subspace information obtained for the symmetric positive definite matrix A
- Multi-grid dynamic iteration for parabolic equations
- RKC: An explicit solver for parabolic PDEs
- Resolvent Krylov subspace approximation to operator functions
- RD-rational approximations of the matrix exponential
- Stability control for approximate implicit time stepping schemes with minimum residual iterations
- Symmetry-preserving discretization of turbulent flow.
- Iterative across-time solution of linear differential equations: Krylov subspace versus waveform relaxation
- An exponential integrator for non-autonomous parabolic problems
- A block Krylov subspace implementation of the time-parallel Paraexp method and its extension for nonlinear partial differential equations
- Residual, Restarting, and Richardson Iteration for the Matrix Exponential
- Exponential integrators
- A block Krylov subspace time-exact solution method for linear ordinary differential equation systems
- Convergence of Dynamic Iteration Methods for Initial Value Problems
- The MATLAB ODE Suite
- Remarks on the convergence of waveform relaxation method
- Spectral Methods in Time for Parabolic Problems
- On the Internal Stability of Explicit,m-Stage Runge-Kutta Methods for Largem-Values
- Efficient Solution of Parabolic Equations by Krylov Approximation Methods
- Explicit difference schemes for solving stiff systems of ODEs and PDEs with complex spectrum
- A Second-Order Rosenbrock Method Applied to Photochemical Dispersion Problems
- Convergence Theory of Nonlinear Newton–Krylov Algorithms
- On Krylov Subspace Approximations to the Matrix Exponential Operator
- An Exponential Time Integrator for the Incompressible Navier--Stokes Equation
- Krylov subspace approximation of eigenpairs and matrix functions in exact and computer arithmetic
- Multigrid Waveform Relaxation of Spatial Finite Element Meshes: The Continuous-Time Case
- PARAEXP: A Parallel Integrator for Linear Initial-Value Problems
- A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
- Algorithm 832
- Preconditioning Lanczos Approximations to the Matrix Exponential
- Difference systems of second order accuracy with a divided operator for parabolic equations without mixed derivatives
- Two polynomial methods of calculating functions of symmetric matrices
- A parallel nearly implicit time-stepping scheme
- Exponential Euler and backward Euler methods for nonlinear heat conduction problems
- Adaptive iterative explicit time integration for nonlinear heat conduction problems
This page was built for publication: On convergence of waveform relaxation for nonlinear systems of ordinary differential equations
