Localized collocation schemes and their applications
Z Fu, Z Tang, Q ** for stiff PDEs
AK Kassam, LN Trefethen - SIAM Journal on Scientific Computing, 2005 - SIAM
A modification of the exponential time-differencing fourth-order Runge--Kutta method for
solving stiff nonlinear PDEs is presented that solves the problem of numerical instability in …
solving stiff nonlinear PDEs is presented that solves the problem of numerical instability in …
Toward an efficient parallel in time method for partial differential equations
M Emmett, M Minion - … in Applied Mathematics and Computational Science, 2012 - msp.org
A new method for the parallelization of numerical methods for partial differential equations
(PDEs) in the temporal direction is presented. The method is iterative with each iteration …
(PDEs) in the temporal direction is presented. The method is iterative with each iteration …
Semi-implicit spectral deferred correction methods for ordinary differential equations
ML Minion - 2003 - projecteuclid.org
A semi-implicit formulation of the method of spectral deferred corrections (SISDC) for
ordinary differential equations with both stiff and non-stiff terms is presented. Several …
ordinary differential equations with both stiff and non-stiff terms is presented. Several …
[HTML][HTML] HPC-enabling technologies for high-fidelity combustion simulations
With the increase in computational power in the last decade and the forthcoming Exascale
supercomputers, a new horizon in computational modelling and simulation is envisioned in …
supercomputers, a new horizon in computational modelling and simulation is envisioned in …
A hybrid parareal spectral deferred corrections method
M Minion - … in Applied Mathematics and Computational Science, 2011 - msp.org
The parareal algorithm introduced in 2001 by Lions, Maday, and Turinici is an iterative
method for the parallelization of the numerical solution of ordinary differential equations or …
method for the parallelization of the numerical solution of ordinary differential equations or …
Sensitivity of He Flames in X-Ray Bursts to Nuclear Physics
Through the use of axisymmetric 2D hydrodynamic simulations, we further investigate
laterally propagating flames in X-ray bursts (XRBs). Our aim is to understand the sensitivity …
laterally propagating flames in X-ray bursts (XRBs). Our aim is to understand the sensitivity …
Deferred correction methods for ordinary differential equations
Deferred correction is a well-established method for incrementally increasing the order of
accuracy of a numerical solution to a set of ordinary differential equations. Because …
accuracy of a numerical solution to a set of ordinary differential equations. Because …
Accelerating the convergence of spectral deferred correction methods
In the recent paper by Dutt, Greengard and Rokhlin, a variant of deferred or defect correction
methods is presented which couples Gaussian quadrature with the Picard integral equation …
methods is presented which couples Gaussian quadrature with the Picard integral equation …