GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A fast algorithm for particle simulations
Journal of Computational Physics
A fast algorithm for the evaluation of Legendre expansions
SIAM Journal on Scientific and Statistical Computing
Spectral integration and two-point boundary value problems
SIAM Journal on Numerical Analysis
Fast algorithms for polynomial interpolation, integration, and differentiation
SIAM Journal on Numerical Analysis
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Avoiding the order reduction of Runge-Kutta methods for linear initial boundary value problems
Mathematics of Computation
High-order multi-implicit spectral deferred correction methods for problems of reactive flow
Journal of Computational Physics
Conservative multi-implicit spectral deferred correction methods for reacting gas dynamics
Journal of Computational Physics
Fractional step methods for index-1 differential-algebraic equations
Journal of Computational Physics
Accelerating the convergence of spectral deferred correction methods
Journal of Computational Physics
Krylov deferred correction accelerated method of lines transpose for parabolic problems
Journal of Computational Physics
Semi-implicit Krylov deferred correction methods for ordinary differential equations
AMATH'09 Proceedings of the 15th american conference on Applied mathematics
Journal of Computational Physics
Parallel High-Order Integrators
SIAM Journal on Scientific Computing
Implicit Parallel Time Integrators
Journal of Scientific Computing
Stable and Spectrally Accurate Schemes for the Navier-Stokes Equations
SIAM Journal on Scientific Computing
An enhanced parareal algorithm based on the deferred correction methods for a stiff system
Journal of Computational and Applied Mathematics
Hi-index | 31.47 |
In this paper, a new framework for the construction of accurate and efficient numerical methods for differential algebraic equation (DAE) initial value problems is presented. The methods are based on applying spectral deferred correction techniques as preconditioners to a Picard integral collocation formulation for the solution. The resulting preconditioned nonlinear system is solved using Newton-Krylov schemes such as the Newton-GMRES method. Least squares based orthogonal polynomial approximations are computed using Gaussian type quadratures, and spectral integration is used to avoid the numerically unstable differentiation operator. The resulting Krylov deferred correction (KDC) methods are of arbitrary order of accuracy and very stable. Preliminary results show that these new methods are very competitive with existing DAE solvers, particularly when high precision is desired.