-
Previous Article
Stochastic modeling of the firing activity of coupled neurons periodically driven
- PROC Home
- This Issue
-
Next Article
Similarity reductions of a nonlinear model for vibrations of beams
Construction of highly stable implicit-explicit general linear methods
1. | Dipartimento di Matematica, Università di Salerno, I-84084 Fisciano (Sa), Italy |
2. | Department of Mathematics, Arizona State University, Tempe, Arizona 85287, and AGH University of Science and Technology, Kraków, Poland |
3. | Department of Computer Science, Virginia Polytechnic Institute & State University, Blacksburg, Virginia 24061, United States |
4. | Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439, United States |
References:
[1] |
U. M. Ascher, S. J. Ruuth and R. J. Spiteri, Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations, Appl. Numer. Math, 25 (1997), 151-167. |
[2] |
U. M. Ascher, S. J. Ruuth and B. T. R. Wetton, Implicit-explicit methods for time-dependent partial differential equations, SIAM J. Numer. Anal., 32 (1995), 797-823. |
[3] |
S. Boscarino, Error analysis of IMEX Runge-Kutta methods derived from differential-algebraic systems, SIAM Journal on Numerical Analysis, 45 (2007), 1600-1621. |
[4] |
S. Boscarino and G. Russo, On a class of uniformly accurate IMEX Runge-Kutta schemes and applications to hyperbolic systems with relaxation, SIAM J. Sci. Comput., 31 (2009), 1926-1945. |
[5] |
M. Braś and A. Cardone, Construction of efficient general linear methods for non-stiff differential systems, Math. Model. Anal., 17 (2012), 171-189. |
[6] |
M. Braś, A. Cardone and R. D'Ambrosio, Implementation of explicit nordsieck methods with inherent quadratic stability, Math. Model. Anal., 18 (2013), 289-307. |
[7] |
J. C. Butcher, Diagonally-implicit multi-stage integration methods, Appl. Numer. Math., 11 (1993), 347-363. |
[8] |
M. P. Calvo, J. de Frutos and J. Novo, Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations, Appl. Numer. Math., 37 (2001), 535-549. |
[9] |
A. Cardone and Z. Jackiewicz, Explicit Nordsieck methods with quadratic stability, Numer. Algorithms, 60 (2012), 1-25. |
[10] |
A. Cardone, Z. Jackiewicz and H. Mittelmann, Optimization-based search for Nordsieck methods of high order with quadratic stability, Math. Model. Anal., 17 (2012), 293-308. |
[11] |
A. Cardone, Z. Jackiewicz, A. Sandu and H. Zhang, Extrapolated implicit-explicit Runge-Kutta methods, Math. Model. Anal., 19 (2014), 18-43. |
[12] |
A. Cardone, Z. Jackiewicz, A. Sandu and H. Zhang, Extrapolation-based implicit-explicit general linear methods, Numer. Algorithms, 65 (2014), 377-399. |
[13] |
J. Frank, W. Hundsdorfer and J. G. Verwer, On the stability of implicit-explicit linear multistep methods, Appl. Numer. Math., 25 (1997), 193-205. |
[14] |
W. Hundsdorfer and S. J. Ruuth, IMEX extensions of linear multistep methods with general monotonicity and boundedness properties, J. Comput. Phys., 225 (2007), 2016-2042. |
[15] |
W. Hundsdorfer and J. Verwer, Numerical solution of time-dependent advection-diffusion-reaction equations, vol. 33 of Springer Series in Comput. Mathematics, Springer-Verlag, 2003. |
[16] |
Z. Jackiewicz, General linear methods for ordinary differential equations, John Wiley & Sons Inc., Hoboken, NJ, 2009. |
[17] |
C. A. Kennedy and M. H. Carpenter, Additive Runge-Kutta schemes for convection-diffusion-reaction equations, Appl. Numer. Math., 44 (2003), 139-181. |
[18] |
L. Pareschi and G. Russo, Implicit-explicit Runge-Kutta schemes for stiff systems of differential equations, in Recent trends in numerical analysis, vol. 3 of Adv. Theory Comput. Math., Nova Sci. Publ., Huntington, NY, 2001, 269-288. |
[19] |
L. Pareschi and G. Russo, Implicit-Explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation, J. Sci. Comput., 25 (2005), 129-155. |
[20] |
W. M. Wright, The construction of order 4 DIMSIMs for ordinary differential equations, Numer. Algorithms, 26 (2001), 123-130. |
[21] |
H. Zhang and A. Sandu, A second-order diagonally-implicit-explicit multi-stage integration method, Procedia CS, 9 (2012), 1039-1046. |
[22] |
H. Zhang, A. Sandu and S. Blaise, High order implicit-explicit general linear methods with optimized stability regions, arXiv preprint, URL http://arxiv.org/abs/1407.2337. |
[23] |
H. Zhang, A. Sandu and S. Blaise, Partitioned and Implicit-Explicit General Linear Methods for ordinary differential equations, J. Sci. Comput., 61 (2014), 119-144. |
[24] |
E. Zharovski, A. Sandu and H. Zhang, A class of implicit-explicit two-step Runge-Kutta methods, SIAM J. Numer. Anal., 53 (2015), no. 1, 321-341. |
show all references
References:
[1] |
U. M. Ascher, S. J. Ruuth and R. J. Spiteri, Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations, Appl. Numer. Math, 25 (1997), 151-167. |
[2] |
U. M. Ascher, S. J. Ruuth and B. T. R. Wetton, Implicit-explicit methods for time-dependent partial differential equations, SIAM J. Numer. Anal., 32 (1995), 797-823. |
[3] |
S. Boscarino, Error analysis of IMEX Runge-Kutta methods derived from differential-algebraic systems, SIAM Journal on Numerical Analysis, 45 (2007), 1600-1621. |
[4] |
S. Boscarino and G. Russo, On a class of uniformly accurate IMEX Runge-Kutta schemes and applications to hyperbolic systems with relaxation, SIAM J. Sci. Comput., 31 (2009), 1926-1945. |
[5] |
M. Braś and A. Cardone, Construction of efficient general linear methods for non-stiff differential systems, Math. Model. Anal., 17 (2012), 171-189. |
[6] |
M. Braś, A. Cardone and R. D'Ambrosio, Implementation of explicit nordsieck methods with inherent quadratic stability, Math. Model. Anal., 18 (2013), 289-307. |
[7] |
J. C. Butcher, Diagonally-implicit multi-stage integration methods, Appl. Numer. Math., 11 (1993), 347-363. |
[8] |
M. P. Calvo, J. de Frutos and J. Novo, Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations, Appl. Numer. Math., 37 (2001), 535-549. |
[9] |
A. Cardone and Z. Jackiewicz, Explicit Nordsieck methods with quadratic stability, Numer. Algorithms, 60 (2012), 1-25. |
[10] |
A. Cardone, Z. Jackiewicz and H. Mittelmann, Optimization-based search for Nordsieck methods of high order with quadratic stability, Math. Model. Anal., 17 (2012), 293-308. |
[11] |
A. Cardone, Z. Jackiewicz, A. Sandu and H. Zhang, Extrapolated implicit-explicit Runge-Kutta methods, Math. Model. Anal., 19 (2014), 18-43. |
[12] |
A. Cardone, Z. Jackiewicz, A. Sandu and H. Zhang, Extrapolation-based implicit-explicit general linear methods, Numer. Algorithms, 65 (2014), 377-399. |
[13] |
J. Frank, W. Hundsdorfer and J. G. Verwer, On the stability of implicit-explicit linear multistep methods, Appl. Numer. Math., 25 (1997), 193-205. |
[14] |
W. Hundsdorfer and S. J. Ruuth, IMEX extensions of linear multistep methods with general monotonicity and boundedness properties, J. Comput. Phys., 225 (2007), 2016-2042. |
[15] |
W. Hundsdorfer and J. Verwer, Numerical solution of time-dependent advection-diffusion-reaction equations, vol. 33 of Springer Series in Comput. Mathematics, Springer-Verlag, 2003. |
[16] |
Z. Jackiewicz, General linear methods for ordinary differential equations, John Wiley & Sons Inc., Hoboken, NJ, 2009. |
[17] |
C. A. Kennedy and M. H. Carpenter, Additive Runge-Kutta schemes for convection-diffusion-reaction equations, Appl. Numer. Math., 44 (2003), 139-181. |
[18] |
L. Pareschi and G. Russo, Implicit-explicit Runge-Kutta schemes for stiff systems of differential equations, in Recent trends in numerical analysis, vol. 3 of Adv. Theory Comput. Math., Nova Sci. Publ., Huntington, NY, 2001, 269-288. |
[19] |
L. Pareschi and G. Russo, Implicit-Explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation, J. Sci. Comput., 25 (2005), 129-155. |
[20] |
W. M. Wright, The construction of order 4 DIMSIMs for ordinary differential equations, Numer. Algorithms, 26 (2001), 123-130. |
[21] |
H. Zhang and A. Sandu, A second-order diagonally-implicit-explicit multi-stage integration method, Procedia CS, 9 (2012), 1039-1046. |
[22] |
H. Zhang, A. Sandu and S. Blaise, High order implicit-explicit general linear methods with optimized stability regions, arXiv preprint, URL http://arxiv.org/abs/1407.2337. |
[23] |
H. Zhang, A. Sandu and S. Blaise, Partitioned and Implicit-Explicit General Linear Methods for ordinary differential equations, J. Sci. Comput., 61 (2014), 119-144. |
[24] |
E. Zharovski, A. Sandu and H. Zhang, A class of implicit-explicit two-step Runge-Kutta methods, SIAM J. Numer. Anal., 53 (2015), no. 1, 321-341. |
[1] |
Andrew J. Steyer, Erik S. Van Vleck. Underlying one-step methods and nonautonomous stability of general linear methods. Discrete and Continuous Dynamical Systems - B, 2018, 23 (7) : 2859-2877. doi: 10.3934/dcdsb.2018108 |
[2] |
Hui Liang, Hermann Brunner. Collocation methods for differential equations with piecewise linear delays. Communications on Pure and Applied Analysis, 2012, 11 (5) : 1839-1857. doi: 10.3934/cpaa.2012.11.1839 |
[3] |
Joseph A. Connolly, Neville J. Ford. Comparison of numerical methods for fractional differential equations. Communications on Pure and Applied Analysis, 2006, 5 (2) : 289-307. doi: 10.3934/cpaa.2006.5.289 |
[4] |
Yuhong Dai, Ya-xiang Yuan. Analysis of monotone gradient methods. Journal of Industrial and Management Optimization, 2005, 1 (2) : 181-192. doi: 10.3934/jimo.2005.1.181 |
[5] |
William Guo. Unification of the common methods for solving the first-order linear ordinary differential equations. STEM Education, 2021, 1 (2) : 127-140. doi: 10.3934/steme.2021010 |
[6] |
Wenxiong Chen, Shijie Qi. Direct methods on fractional equations. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 1269-1310. doi: 10.3934/dcds.2019055 |
[7] |
Konstantinos Drakakis. A review of the available construction methods for Golomb rulers. Advances in Mathematics of Communications, 2009, 3 (3) : 235-250. doi: 10.3934/amc.2009.3.235 |
[8] |
Robert Baier, Thuy T. T. Le. Construction of the minimum time function for linear systems via higher-order set-valued methods. Mathematical Control and Related Fields, 2019, 9 (2) : 223-255. doi: 10.3934/mcrf.2019012 |
[9] |
Yoonsang Lee, Bjorn Engquist. Variable step size multiscale methods for stiff and highly oscillatory dynamical systems. Discrete and Continuous Dynamical Systems, 2014, 34 (3) : 1079-1097. doi: 10.3934/dcds.2014.34.1079 |
[10] |
Yixuan Wu, Yanzhi Zhang. Highly accurate operator factorization methods for the integral fractional Laplacian and its generalization. Discrete and Continuous Dynamical Systems - S, 2022, 15 (4) : 851-876. doi: 10.3934/dcdss.2022016 |
[11] |
Angelamaria Cardone, Dajana Conte, Beatrice Paternoster. Two-step collocation methods for fractional differential equations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (7) : 2709-2725. doi: 10.3934/dcdsb.2018088 |
[12] |
Iasson Karafyllis, Lars Grüne. Feedback stabilization methods for the numerical solution of ordinary differential equations. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 283-317. doi: 10.3934/dcdsb.2011.16.283 |
[13] |
Xiaobing Feng, Shu Ma. Stable numerical methods for a stochastic nonlinear Schrödinger equation with linear multiplicative noise. Discrete and Continuous Dynamical Systems - S, 2022, 15 (4) : 687-711. doi: 10.3934/dcdss.2021071 |
[14] |
B. S. Goh, W. J. Leong, Z. Siri. Partial Newton methods for a system of equations. Numerical Algebra, Control and Optimization, 2013, 3 (3) : 463-469. doi: 10.3934/naco.2013.3.463 |
[15] |
Xiangtuan Xiong, Jinmei Li, Jin Wen. Some novel linear regularization methods for a deblurring problem. Inverse Problems and Imaging, 2017, 11 (2) : 403-426. doi: 10.3934/ipi.2017019 |
[16] |
Daijun Jiang, Hui Feng, Jun Zou. Overlapping domain decomposition methods for linear inverse problems. Inverse Problems and Imaging, 2015, 9 (1) : 163-188. doi: 10.3934/ipi.2015.9.163 |
[17] |
Ji-Woong Jang, Young-Sik Kim, Sang-Hyo Kim, Dae-Woon Lim. New construction methods of quaternary periodic complementary sequence sets. Advances in Mathematics of Communications, 2010, 4 (1) : 61-68. doi: 10.3934/amc.2010.4.61 |
[18] |
Jiangshan Wang, Lingxiong Meng, Hongen Jia. Numerical analysis of modular grad-div stability methods for the time-dependent Navier-Stokes/Darcy model. Electronic Research Archive, 2020, 28 (3) : 1191-1205. doi: 10.3934/era.2020065 |
[19] |
Antonella Zanna. Symplectic P-stable additive Runge—Kutta methods. Journal of Computational Dynamics, 2022, 9 (2) : 299-328. doi: 10.3934/jcd.2021030 |
[20] |
M. Sumon Hossain, M. Monir Uddin. Iterative methods for solving large sparse Lyapunov equations and application to model reduction of index 1 differential-algebraic-equations. Numerical Algebra, Control and Optimization, 2019, 9 (2) : 173-186. doi: 10.3934/naco.2019013 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]