Rosenbrock-W methods for stochastic Galerkin systems

Pulch, Roland; Sandu, Adrian

doi:10.1016/j.cam.2023.115527

Title: Rosenbrock-W methods for stochastic Galerkin systems

Journal Article · 01 March 2024 · Journal of Computational and Applied Mathematics

DOI: https://doi.org/10.1016/j.cam.2023.115527 · OSTI ID:2369784

Pulch, Roland; Sandu, Adrian

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Sponsoring Organization:: USDOE

OSTI ID:: 2369784

Journal Information:: Journal of Computational and Applied Mathematics, Journal Name: Journal of Computational and Applied Mathematics Journal Issue: C Vol. 438; ISSN 0377-0427

Publisher:: ElsevierCopyright Statement

Country of Publication:: Belgium

Language:: English

References (12)

Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations Kaps, Peter; Rentrop, Peter Numerische Mathematik, Vol. 33, Issue 1 https://doi.org/10.1007/BF01396495	journal	March 1979
Stochastic Galerkin techniques for random ordinary differential equations Augustin, F.; Rentrop, P. Numerische Mathematik, Vol. 122, Issue 3 https://doi.org/10.1007/s00211-012-0466-8	journal	April 2012
New Rosenbrock W-Methods of Order 3 for Partial Differential Algebraic Equations of Index 1 Rang, J.; Angermann, L. BIT Numerical Mathematics, Vol. 45, Issue 4 https://doi.org/10.1007/s10543-005-0035-y	journal	December 2005
The logarithmic norm. History and modern theory Söderlind, Gustaf BIT Numerical Mathematics, Vol. 46, Issue 3 https://doi.org/10.1007/s10543-006-0069-9	journal	August 2006
A new approximate matrix factorization for implicit time integration in air pollution modeling Botchev, M. A.; Verwer, J. G. Journal of Computational and Applied Mathematics, Vol. 157, Issue 2 https://doi.org/10.1016/S0377-0427(03)00414-X	journal	August 2003
High-order W-methods Rahunanthan, Arunasalam; Stanescu, Dan Journal of Computational and Applied Mathematics, Vol. 233, Issue 8 https://doi.org/10.1016/j.cam.2009.09.017	journal	February 2010
Stochastic collocation and stochastic Galerkin methods for linear differential algebraic equations Pulch, Roland Journal of Computational and Applied Mathematics, Vol. 262 https://doi.org/10.1016/j.cam.2013.10.046	journal	May 2014
Improved traditional Rosenbrock–Wanner methods for stiff ODEs and DAEs Rang, Joachim Journal of Computational and Applied Mathematics, Vol. 286 https://doi.org/10.1016/j.cam.2015.03.010	journal	October 2015
Efficient uncertainty quantification with the polynomial chaos method for stiff systems Cheng, Haiyan; Sandu, Adrian Mathematics and Computers in Simulation, Vol. 79, Issue 11 https://doi.org/10.1016/j.matcom.2009.05.002	journal	July 2009
An attempt to avoid exact Jacobian and nonlinear equations in the numerical solution of stiff differential equations Steihaug, Trond; Wolfbrandt, Arne Mathematics of Computation, Vol. 33, Issue 146 https://doi.org/10.1090/S0025-5718-1979-0521273-8	journal	May 1979
Eigenvalues of the Jacobian of a Galerkin-Projected Uncertain ODE System Sonday, Benjamin E.; Berry, Robert D.; Najm, Habib N. SIAM Journal on Scientific Computing, Vol. 33, Issue 3 https://doi.org/10.1137/100785922	journal	January 2011
Stochastic Galerkin Methods for Analyzing Equilibria of Random Dynamical Systems Pulch, Roland SIAM/ASA Journal on Uncertainty Quantification, Vol. 1, Issue 1 https://doi.org/10.1137/130923543	journal	January 2013

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