Nan, Caixia; Song, Huailing A new high-order maximum-principle-preserving explicit Runge-Kutta method for the nonlocal Allen-Cahn equation. (English) Zbl 1522.65221 J. Comput. Appl. Math. 437, Article ID 115500, 19 p. (2024). MSC: 65N30 65N12 PDFBibTeX XMLCite \textit{C. Nan} and \textit{H. Song}, J. Comput. Appl. Math. 437, Article ID 115500, 19 p. (2024; Zbl 1522.65221) Full Text: DOI
Orlando, Giuseppe A filtering monotonization approach for DG discretizations of hyperbolic problems. (English) Zbl 1524.65581 Comput. Math. Appl. 129, 113-125 (2023). MSC: 65M60 35L65 65N30 76M10 65M12 35F21 35Q31 76N10 76B03 65L06 65M06 PDFBibTeX XMLCite \textit{G. Orlando}, Comput. Math. Appl. 129, 113--125 (2023; Zbl 1524.65581) Full Text: DOI arXiv
Santiago, D. F. G.; Antunis, A. F.; Trindade, D. R.; Brandão, W. J. S. Strong stability preserving Runge-Kutta methods applied to water hammer problem. (English) Zbl 1527.65053 Trends Comput. Appl. Math. 23, No. 1, 63-77 (2022). MSC: 65L06 PDFBibTeX XMLCite \textit{D. F. G. Santiago} et al., Trends Comput. Appl. Math. 23, No. 1, 63--77 (2022; Zbl 1527.65053) Full Text: DOI
Ern, Alexandre; Guermond, Jean-Luc Invariant-domain-preserving high-order time stepping. I: Explicit Runge-Kutta schemes. (English) Zbl 1501.65070 SIAM J. Sci. Comput. 44, No. 5, A3366-A3392 (2022). Reviewer: Bülent Karasözen (Ankara) MSC: 65M60 65L06 65M06 65N30 35L65 65M12 PDFBibTeX XMLCite \textit{A. Ern} and \textit{J.-L. Guermond}, SIAM J. Sci. Comput. 44, No. 5, A3366--A3392 (2022; Zbl 1501.65070) Full Text: DOI
Shallu; Kukreja, Vijay Kumar An efficient collocation algorithm with SSP-RK43 scheme to solve Rosenau-KdV-RLW equation. (English) Zbl 1502.65163 Int. J. Appl. Comput. Math. 7, No. 4, Paper No. 161, 18 p. (2021). MSC: 65M70 35Q35 65D07 65L06 76B15 PDFBibTeX XMLCite \textit{Shallu} and \textit{V. K. Kukreja}, Int. J. Appl. Comput. Math. 7, No. 4, Paper No. 161, 18 p. (2021; Zbl 1502.65163) Full Text: DOI
Yeager, Benjamin; Kubatko, Ethan; Wood, Dylan Time step restrictions for strong-stability-preserving multistep Runge-Kutta discontinuous Galerkin methods. (English) Zbl 1514.65136 J. Sci. Comput. 89, No. 2, Paper No. 29, 18 p. (2021). MSC: 65M60 65L06 65M06 65N30 65M20 65M12 49M41 PDFBibTeX XMLCite \textit{B. Yeager} et al., J. Sci. Comput. 89, No. 2, Paper No. 29, 18 p. (2021; Zbl 1514.65136) Full Text: DOI
Higueras, I.; Roldán, T. Efficient SSP low-storage Runge-Kutta methods. (English) Zbl 1458.65085 J. Comput. Appl. Math. 387, Article ID 112500, 15 p. (2021). MSC: 65L06 65L04 65L05 65L20 PDFBibTeX XMLCite \textit{I. Higueras} and \textit{T. Roldán}, J. Comput. Appl. Math. 387, Article ID 112500, 15 p. (2021; Zbl 1458.65085) Full Text: DOI
Hoang, Thi-Thao-Phuong; Leng, Wei; Ju, Lili; Wang, Zhu; Pieper, Konstantin Conservative explicit local time-stepping schemes for the shallow water equations. (English) Zbl 1451.65133 J. Comput. Phys. 382, 152-176 (2019). MSC: 65M22 86A05 65M06 65M08 PDFBibTeX XMLCite \textit{T.-T.-P. Hoang} et al., J. Comput. Phys. 382, 152--176 (2019; Zbl 1451.65133) Full Text: DOI Link
Ranocha, Hendrik Some notes on summation by parts time integration methods. (English) Zbl 1453.65161 Results Appl. Math. 1, Article ID 100004, 3 p. (2019). MSC: 65L05 65L06 65L20 PDFBibTeX XMLCite \textit{H. Ranocha}, Results Appl. Math. 1, Article ID 100004, 3 p. (2019; Zbl 1453.65161) Full Text: DOI arXiv
Grant, Zachary; Gottlieb, Sigal; Seal, David C. A strong stability preserving analysis for explicit multistage two-derivative time-stepping schemes based on Taylor series conditions. (English) Zbl 1449.65223 Commun. Appl. Math. Comput. 1, No. 1, 21-59 (2019). MSC: 65M20 65M12 65L06 65L20 65N06 65K10 PDFBibTeX XMLCite \textit{Z. Grant} et al., Commun. Appl. Math. Comput. 1, No. 1, 21--59 (2019; Zbl 1449.65223) Full Text: DOI arXiv Link
Higueras, I.; Roldán, T. Strong stability preserving properties of composition Runge-Kutta schemes. (English) Zbl 1416.65193 J. Sci. Comput. 80, No. 2, 784-807 (2019). MSC: 65L05 65L06 65L20 65M20 PDFBibTeX XMLCite \textit{I. Higueras} and \textit{T. Roldán}, J. Sci. Comput. 80, No. 2, 784--807 (2019; Zbl 1416.65193) Full Text: DOI
Giuliani, Andrew; Krivodonova, Lilia On the optimal CFL number of SSP methods for hyperbolic problems. (English) Zbl 1406.65079 Appl. Numer. Math. 135, 165-172 (2019). MSC: 65M20 65M08 65L06 65M12 35L65 PDFBibTeX XMLCite \textit{A. Giuliani} and \textit{L. Krivodonova}, Appl. Numer. Math. 135, 165--172 (2019; Zbl 1406.65079) Full Text: DOI Link
Nguyen-Ba, Truong; Giordano, Thierry; Vaillancourt, Rémi On Runge-Kutta-Nystrom formulae with contractivity preserving properties for second order ODEs. (English) Zbl 1424.65101 Acta Univ. Apulensis, Math. Inform. 54, 89-113 (2018). MSC: 65L06 PDFBibTeX XMLCite \textit{T. Nguyen-Ba} et al., Acta Univ. Apulensis, Math. Inform. 54, 89--113 (2018; Zbl 1424.65101) Full Text: DOI
Higueras, Inmaculada; Ketcheson, David I.; Kocsis, Tihamér A. Optimal monotonicity-preserving perturbations of a given Runge-Kutta method. (English) Zbl 1397.65103 J. Sci. Comput. 76, No. 3, 1337-1369 (2018). MSC: 65L06 65L20 65M20 PDFBibTeX XMLCite \textit{I. Higueras} et al., J. Sci. Comput. 76, No. 3, 1337--1369 (2018; Zbl 1397.65103) Full Text: DOI arXiv
Hadjimichael, Yiannis; Ketcheson, David I. Strong-stability-preserving additive linear multistep methods. (English) Zbl 1458.65084 Math. Comput. 87, No. 313, 2295-2320 (2018). MSC: 65L06 65L05 65M20 PDFBibTeX XMLCite \textit{Y. Hadjimichael} and \textit{D. I. Ketcheson}, Math. Comput. 87, No. 313, 2295--2320 (2018; Zbl 1458.65084) Full Text: DOI arXiv
Fekete, Imre; Ketcheson, David I.; Lóczi, Lajos Positivity for convective semi-discretizations. (English) Zbl 1419.65043 J. Sci. Comput. 74, No. 1, 244-266 (2018). Reviewer: Petr Sváček (Praha) MSC: 65M20 65M12 PDFBibTeX XMLCite \textit{I. Fekete} et al., J. Sci. Comput. 74, No. 1, 244--266 (2018; Zbl 1419.65043) Full Text: DOI arXiv
Conde, Sidafa; Gottlieb, Sigal; Grant, Zachary J.; Shadid, John N. Implicit and implicit-explicit strong stability preserving Runge-Kutta methods with high linear order. (English) Zbl 1381.65052 J. Sci. Comput. 73, No. 2-3, 667-690 (2017). MSC: 65L05 35L65 65L06 65L20 65M20 34A34 PDFBibTeX XMLCite \textit{S. Conde} et al., J. Sci. Comput. 73, No. 2--3, 667--690 (2017; Zbl 1381.65052) Full Text: DOI arXiv
Nguyen-Ba, Truong; Giordano, Thierry; Nguyen-Thu, Huong; Vaillancourt, Rémi On contractivity preserving 4- to 7-step predictor-corrector HBO series for ODEs. (English) Zbl 1422.65114 J. Mod. Methods Numer. Math. 8, No. 1-2, 139-155 (2017). MSC: 65L06 65D05 65D30 PDFBibTeX XMLCite \textit{T. Nguyen-Ba} et al., J. Mod. Methods Numer. Math. 8, No. 1--2, 139--155 (2017; Zbl 1422.65114) Full Text: DOI
Bashan, Ali; Yagmurlu, Nuri Murat; Ucar, Yusuf; Esen, Alaattin An effective approach to numerical soliton solutions for the Schrödinger equation via modified cubic B-spline differential quadrature method. (English) Zbl 1422.65294 Chaos Solitons Fractals 100, 45-56 (2017). MSC: 65M99 65D07 65L06 35C08 35Q55 PDFBibTeX XMLCite \textit{A. Bashan} et al., Chaos Solitons Fractals 100, 45--56 (2017; Zbl 1422.65294) Full Text: DOI
Spijker, M. N. Stability and boundedness in the numerical solution of initial value problems. (English) Zbl 1368.65122 Math. Comput. 86, No. 308, 2777-2798 (2017). MSC: 65L20 65M12 65L05 34A30 65M20 65L06 35K15 PDFBibTeX XMLCite \textit{M. N. Spijker}, Math. Comput. 86, No. 308, 2777--2798 (2017; Zbl 1368.65122) Full Text: DOI Link
Mittal, R. C.; Tripathi, Amit Numerical solutions of two-dimensional unsteady convection-diffusion problems using modified bi-cubic B-spline finite elements. (English) Zbl 1365.65229 Int. J. Comput. Math. 94, No. 1, 1-21 (2017). MSC: 65M70 35K20 65Y20 65M12 65L06 65M60 PDFBibTeX XMLCite \textit{R. C. Mittal} and \textit{A. Tripathi}, Int. J. Comput. Math. 94, No. 1, 1--21 (2017; Zbl 1365.65229) Full Text: DOI
Bonaventura, L.; Della Rocca, A. Unconditionally strong stability preserving extensions of the TR-BDF2 method. (English) Zbl 1361.65046 J. Sci. Comput. 70, No. 2, 859-895 (2017). MSC: 65L05 65L04 65L06 34A34 65L20 PDFBibTeX XMLCite \textit{L. Bonaventura} and \textit{A. Della Rocca}, J. Sci. Comput. 70, No. 2, 859--895 (2017; Zbl 1361.65046) Full Text: DOI Link
Izzo, Giuseppe; Jackiewicz, Zdzislaw Highly stable implicit-explicit Runge-Kutta methods. (English) Zbl 1355.65096 Appl. Numer. Math. 113, 71-92 (2017). MSC: 65L06 65L05 65L20 65L04 34A34 65M20 35L65 PDFBibTeX XMLCite \textit{G. Izzo} and \textit{Z. Jackiewicz}, Appl. Numer. Math. 113, 71--92 (2017; Zbl 1355.65096) Full Text: DOI
Christlieb, Andrew J.; Gottlieb, Sigal; Grant, Zachary; Seal, David C. Explicit strong stability preserving multistage two-derivative time-stepping schemes. (English) Zbl 1352.65289 J. Sci. Comput. 68, No. 3, 914-942 (2016); erratum ibid. 68, No. 3, 943-944 (2016). MSC: 65M12 65M06 65M20 35L65 PDFBibTeX XMLCite \textit{A. J. Christlieb} et al., J. Sci. Comput. 68, No. 3, 914--942 (2016; Zbl 1352.65289) Full Text: DOI DOI arXiv
Higueras, Inmaculada; Roldán, Teo Construction of additive semi-implicit Runge-Kutta methods with low-storage requirements. (English) Zbl 1342.65161 J. Sci. Comput. 67, No. 3, 1019-1042 (2016). MSC: 65L06 65M20 65L04 65L05 65L20 34A34 PDFBibTeX XMLCite \textit{I. Higueras} and \textit{T. Roldán}, J. Sci. Comput. 67, No. 3, 1019--1042 (2016; Zbl 1342.65161) Full Text: DOI arXiv
Izzo, Giuseppe; Jackiewicz, Zdzislaw Strong stability preserving multistage integration methods. (English) Zbl 1488.65175 Math. Model. Anal. 20, No. 5, 552-577 (2015). MSC: 65L06 65L20 65L99 65M20 PDFBibTeX XMLCite \textit{G. Izzo} and \textit{Z. Jackiewicz}, Math. Model. Anal. 20, No. 5, 552--577 (2015; Zbl 1488.65175) Full Text: DOI
Gottlieb, Sigal Strong stability preserving time discretizations: a review. (English) Zbl 1352.65291 Kirby, Robert M. (ed.) et al., Spectral and high order methods for partial differential equations, ICOSAHOM 2014. Selected papers from the ICOSAHOM conference, June 23–27, 2014, Salt Lake City, UT, USA. Cham: Springer (ISBN 978-3-319-19799-9/hbk; 978-3-319-19800-2/ebook). Lecture Notes in Computational Science and Engineering 106, 17-30 (2015). Reviewer: Irina V. Konopleva (Ul’yanovsk) MSC: 65M12 65L06 65M20 35L65 65-02 PDFBibTeX XMLCite \textit{S. Gottlieb}, Lect. Notes Comput. Sci. Eng. 106, 17--30 (2015; Zbl 1352.65291) Full Text: DOI
Mittal, R. C.; Dahiya, Sumita Numerical solutions of differential equations using modified B-spline differential quadrature method. (English) Zbl 1337.65090 Agrawal, P. N. (ed.) et al., Mathematical analysis and its applications. Proceedings of the international conference on recent trends in mathematical analyis and its applications, ICRTMAA 2014, Roorkee, India, December 21–23, 2014. New Delhi: Springer (ISBN 978-81-322-2484-6/hbk; 978-81-322-2485-3/ebook). Springer Proceedings in Mathematics & Statistics 143, 509-523 (2015). MSC: 65L10 35K05 35L05 65M20 65L06 65M12 65L20 PDFBibTeX XMLCite \textit{R. C. Mittal} and \textit{S. Dahiya}, Springer Proc. Math. Stat. 143, 509--523 (2015; Zbl 1337.65090) Full Text: DOI
Gottlieb, Sigal; Grant, Zachary; Higgs, Daniel Optimal explicit strong stability preserving Runge-Kutta methods with high linear order and optimal nonlinear order. (English) Zbl 1321.65138 Math. Comput. 84, No. 296, 2743-2761 (2015). MSC: 65M12 65M20 65L06 35L70 PDFBibTeX XMLCite \textit{S. Gottlieb} et al., Math. Comput. 84, No. 296, 2743--2761 (2015; Zbl 1321.65138) Full Text: DOI arXiv
Mittal, R. C.; Tripathi, Amit Numerical solutions of generalized Burgers-Fisher and generalized Burgers-Huxley equations using collocation of cubic \(B\)-splines. (English) Zbl 1314.65134 Int. J. Comput. Math. 92, No. 5, 1053-1077 (2015). MSC: 65M70 65M12 35Q53 PDFBibTeX XMLCite \textit{R. C. Mittal} and \textit{A. Tripathi}, Int. J. Comput. Math. 92, No. 5, 1053--1077 (2015; Zbl 1314.65134) Full Text: DOI
Mozartova, A.; Savostianov, I.; Hundsdorfer, W. Comparison of boundedness and monotonicity properties of one-leg and linear multistep methods. (English) Zbl 1306.65228 J. Comput. Appl. Math. 279, 159-172 (2015). MSC: 65L06 65L05 65L50 34A34 35K55 PDFBibTeX XMLCite \textit{A. Mozartova} et al., J. Comput. Appl. Math. 279, 159--172 (2015; Zbl 1306.65228) Full Text: DOI
Kubatko, Ethan J.; Yeager, Benjamin A.; Ketcheson, David I. Optimal strong-stability-preserving Runge-Kutta time discretizations for discontinuous Galerkin methods. (English) Zbl 1304.65219 J. Sci. Comput. 60, No. 2, 313-344 (2014). MSC: 65M60 65L06 65M20 65M12 35L65 PDFBibTeX XMLCite \textit{E. J. Kubatko} et al., J. Sci. Comput. 60, No. 2, 313--344 (2014; Zbl 1304.65219) Full Text: DOI
Hai, Doan Duy; Yagi, Atsushi Rosenbrock strong stability-preserving methods for convection-diffusion-reaction equations. (English) Zbl 1297.65082 Japan J. Ind. Appl. Math. 31, No. 2, 401-417 (2014). MSC: 65L06 34A34 65L05 35L57 65L20 65M12 65M20 92C17 PDFBibTeX XMLCite \textit{D. D. Hai} and \textit{A. Yagi}, Japan J. Ind. Appl. Math. 31, No. 2, 401--417 (2014; Zbl 1297.65082) Full Text: DOI
Higueras, Inmaculada; Happenhofer, Natalie; Koch, Othmar; Kupka, Friedrich Optimized strong stability preserving IMEX Runge-Kutta methods. (English) Zbl 1294.65076 J. Comput. Appl. Math. 272, 116-140 (2014). MSC: 65L06 65L05 34A34 65M20 35L60 65L20 85A05 PDFBibTeX XMLCite \textit{I. Higueras} et al., J. Comput. Appl. Math. 272, 116--140 (2014; Zbl 1294.65076) Full Text: DOI
Nguyen-Thu, Huong; Nguyen-Ba, Truong; Vaillancourt, Rémi Strong-stability-preserving, Hermite-Birkhoff time-discretization based on \(k\) step methods and 8-stage explicit Runge-Kutta methods of order 5 and 4. (English) Zbl 1301.65074 J. Comput. Appl. Math. 263, 45-58 (2014). MSC: 65L06 65M20 65L20 PDFBibTeX XMLCite \textit{H. Nguyen-Thu} et al., J. Comput. Appl. Math. 263, 45--58 (2014; Zbl 1301.65074) Full Text: DOI
Ketcheson, David I.; Macdonald, Colin B.; Ruuth, Steven J. Spatially partitioned embedded Runge-Kutta methods. (English) Zbl 1285.65061 SIAM J. Numer. Anal. 51, No. 5, 2887-2910 (2013). Reviewer: Fernando Casas (Castellon) MSC: 65M20 35L65 65L06 65M12 PDFBibTeX XMLCite \textit{D. I. Ketcheson} et al., SIAM J. Numer. Anal. 51, No. 5, 2887--2910 (2013; Zbl 1285.65061) Full Text: DOI arXiv
Hadjimichael, Yiannis; Macdonald, Colin B.; Ketcheson, David I.; Verner, James H. Strong stability preserving explicit Runge-Kutta methods of maximal effective order. (English) Zbl 1278.65116 SIAM J. Numer. Anal. 51, No. 4, 2149-2165 (2013). Reviewer: Qin Meng Zhao (Beijing) MSC: 65L20 65M20 65L06 34A34 65L05 PDFBibTeX XMLCite \textit{Y. Hadjimichael} et al., SIAM J. Numer. Anal. 51, No. 4, 2149--2165 (2013; Zbl 1278.65116) Full Text: DOI arXiv
Spijker, M. N. The existence of stepsize-coefficients for boundedness of linear multistep methods. (English) Zbl 1255.65136 Appl. Numer. Math. 63, 45-57 (2013). MSC: 65L06 PDFBibTeX XMLCite \textit{M. N. Spijker}, Appl. Numer. Math. 63, 45--57 (2013; Zbl 1255.65136) Full Text: DOI
Hundsdorfer, W.; Mozartova, A.; Spijker, M. N. Stepsize restrictions for boundedness and monotonicity of multistep methods. (English) Zbl 1261.65084 J. Sci. Comput. 50, No. 2, 265-286 (2012). Reviewer: Vu Hoang Linh (Hanoi) MSC: 65L50 65L06 65L05 65L20 34A34 PDFBibTeX XMLCite \textit{W. Hundsdorfer} et al., J. Sci. Comput. 50, No. 2, 265--286 (2012; Zbl 1261.65084) Full Text: DOI Link
Mittal, R. C.; Jain, R. K. Numerical solutions of nonlinear Burgers equation with modified cubic B-splines collocation method. (English) Zbl 1242.65209 Appl. Math. Comput. 218, No. 15, 7839-7855 (2012). MSC: 65M70 35Q53 65L06 65M30 PDFBibTeX XMLCite \textit{R. C. Mittal} and \textit{R. K. Jain}, Appl. Math. Comput. 218, No. 15, 7839--7855 (2012; Zbl 1242.65209) Full Text: DOI
Sari, Murat Differential quadrature solutions of the generalized Burgers-Fisher equation with a strong stability preserving high-order time integration. (English) Zbl 1246.65192 Math. Comput. Appl. 16, No. 2, 477-486 (2011). MSC: 65M99 35Q53 65L06 65M12 PDFBibTeX XMLCite \textit{M. Sari}, Math. Comput. Appl. 16, No. 2, 477--486 (2011; Zbl 1246.65192) Full Text: DOI
Ketcheson, David I.; Gottlieb, Sigal; Macdonald, Colin B. Strong stability preserving two-step Runge-Kutta methods. (English) Zbl 1240.65278 SIAM J. Numer. Anal. 49, No. 6, 2618-2639 (2011). Reviewer: Fernando Casas (Castellon) MSC: 65M20 65L06 65M06 65M12 35L65 PDFBibTeX XMLCite \textit{D. I. Ketcheson} et al., SIAM J. Numer. Anal. 49, No. 6, 2618--2639 (2011; Zbl 1240.65278) Full Text: DOI arXiv
Hundsdorfer, W.; Mozartova, A.; Spijker, M. N. Special boundedness properties in numerical initial value problems. (English) Zbl 1239.65045 BIT 51, No. 4, 909-936 (2011). Reviewer: Manuel Calvo (Zaragoza) MSC: 65L05 65L06 65L20 65M20 65M12 34A34 65L50 PDFBibTeX XMLCite \textit{W. Hundsdorfer} et al., BIT 51, No. 4, 909--936 (2011; Zbl 1239.65045) Full Text: DOI Link
Ketcheson, David I. Step sizes for strong stability preservation with downwind-biased operators. (English) Zbl 1229.65136 SIAM J. Numer. Anal. 49, No. 4, 1649-1660 (2011). Reviewer: Kai Diethelm (Braunschweig) MSC: 65L20 65L07 65L06 65L05 65L70 34D20 34A34 65M20 PDFBibTeX XMLCite \textit{D. I. Ketcheson}, SIAM J. Numer. Anal. 49, No. 4, 1649--1660 (2011; Zbl 1229.65136) Full Text: DOI arXiv
Gürarslan, Gürhan; Sari, Murat Numerical solutions of linear and nonlinear diffusion equations by a differential quadrature method (DQM). (English) Zbl 1210.65175 Int. J. Numer. Methods Biomed. Eng. 27, No. 1, 69-77 (2011). MSC: 65M70 35K05 35K55 65M12 PDFBibTeX XMLCite \textit{G. Gürarslan} and \textit{M. Sari}, Int. J. Numer. Methods Biomed. Eng. 27, No. 1, 69--77 (2011; Zbl 1210.65175) Full Text: DOI
Constantinescu, Emil M.; Sandu, Adrian Optimal explicit strong-stability-preserving general linear methods. (English) Zbl 1217.65179 SIAM J. Sci. Comput. 32, No. 5, 3130-3150 (2010). MSC: 65M20 65M12 35Q53 35L65 65L06 PDFBibTeX XMLCite \textit{E. M. Constantinescu} and \textit{A. Sandu}, SIAM J. Sci. Comput. 32, No. 5, 3130--3150 (2010; Zbl 1217.65179) Full Text: DOI Link
Higueras, Inmaculada Characterizing strong stability preserving additive Runge-Kutta methods. (English) Zbl 1203.65109 J. Sci. Comput. 39, No. 1, 115-128 (2009). MSC: 65L06 65M20 PDFBibTeX XMLCite \textit{I. Higueras}, J. Sci. Comput. 39, No. 1, 115--128 (2009; Zbl 1203.65109) Full Text: DOI
Hundsdorfer, W.; Mozartova, A.; Spijker, M. N. Stepsize conditions for boundedness in numerical initial value problems. (English) Zbl 1209.65074 SIAM J. Numer. Anal. 47, No. 5, 3797-3819 (2009). Reviewer: Tomas Vejchodsky (Praha) MSC: 65L06 65L05 65L20 65M20 34A34 PDFBibTeX XMLCite \textit{W. Hundsdorfer} et al., SIAM J. Numer. Anal. 47, No. 5, 3797--3819 (2009; Zbl 1209.65074) Full Text: DOI Link
Banda, M. K. Implicit-explicit (IMEX) schemes and relaxation systems. (English) Zbl 1175.65107 Abdulle, Assyr (ed.) et al., Multiple scales problems in biomathematics, mechanics, physics and numerics, CIMPA school, Cape Town, South Africa, August 6–18, 2007. Tokyo: Gakkotosho (ISBN 978-4-7625-0456-3/hbk). GAKUTO International Series. Mathematical Sciences and Applications 31, 301-325 (2009). MSC: 65M20 35L65 35B25 65M06 65M12 PDFBibTeX XMLCite \textit{M. K. Banda}, GAKUTO Int. Ser., Math. Sci. Appl. 31, 301--325 (2009; Zbl 1175.65107)
Macdonald, Colin B.; Gottlieb, Sigal; Ruuth, Steven J. A numerical study of diagonally split Runge-Kutta methods for PDEs with discontinuities. (English) Zbl 1203.65167 J. Sci. Comput. 36, No. 1, 89-112 (2008). MSC: 65M20 65L06 65L20 PDFBibTeX XMLCite \textit{C. B. Macdonald} et al., J. Sci. Comput. 36, No. 1, 89--112 (2008; Zbl 1203.65167) Full Text: DOI
Ketcheson, David I. Highly efficient strong stability-preserving Runge-Kutta methods with low-storage implementations. (English) Zbl 1168.65382 SIAM J. Sci. Comput. 30, No. 4, 2113-2136 (2008). MSC: 65M20 35K55 65L06 65M50 PDFBibTeX XMLCite \textit{D. I. Ketcheson}, SIAM J. Sci. Comput. 30, No. 4, 2113--2136 (2008; Zbl 1168.65382) Full Text: DOI
Kubatko, Ethan J.; Dawson, Clint; Westerink, Joannes J. Time step restrictions for Runge-Kutta discontinuous Galerkin methods on triangular grids. (English) Zbl 1154.65071 J. Comput. Phys. 227, No. 23, 9697-9710 (2008). MSC: 65M20 65M60 65L06 65M12 65Y20 35K15 PDFBibTeX XMLCite \textit{E. J. Kubatko} et al., J. Comput. Phys. 227, No. 23, 9697--9710 (2008; Zbl 1154.65071) Full Text: DOI
Ferracina, L.; Spijker, M. N. Strong stability of singly-diagonally-implicit Runge-Kutta methods. (English) Zbl 1153.65080 Appl. Numer. Math. 58, No. 11, 1675-1686 (2008). Reviewer: M. Gousidou-Koutita (Thessaloniki) MSC: 65L20 65L06 65L05 65M20 PDFBibTeX XMLCite \textit{L. Ferracina} and \textit{M. N. Spijker}, Appl. Numer. Math. 58, No. 11, 1675--1686 (2008; Zbl 1153.65080) Full Text: DOI
Wang, Rong; Spiteri, Raymond J. Linear instability of the fifth-order WENO method. (English) Zbl 1158.65065 SIAM J. Numer. Anal. 45, No. 5, 1871-1901 (2007). Reviewer: Yaşar Sözen (Istanbul) MSC: 65M12 65M06 65L06 35L65 65M20 PDFBibTeX XMLCite \textit{R. Wang} and \textit{R. J. Spiteri}, SIAM J. Numer. Anal. 45, No. 5, 1871--1901 (2007; Zbl 1158.65065) Full Text: DOI
Spijker, M. N. Stepsize conditions for general monotonicity in numerical initial value problems. (English) Zbl 1144.65055 SIAM J. Numer. Anal. 45, No. 3, 1226-1245 (2007). Reviewer: Othmar Koch (Baden) MSC: 65L50 65L05 65L06 65L20 34A34 PDFBibTeX XMLCite \textit{M. N. Spijker}, SIAM J. Numer. Anal. 45, No. 3, 1226--1245 (2007; Zbl 1144.65055) Full Text: DOI
Sármány, D.; Botchev, M. A.; van der Vegt, J. J. W. Dispersion and dissipation error in high-order Runge-Kutta discontinuous Galerkin discretisations of the Maxwell equations. (English) Zbl 1128.78014 J. Sci. Comput. 33, No. 1, 47-74 (2007). Reviewer: Teodora-Liliana Rădulescu (Craiova) MSC: 78M25 78A25 49M15 65L06 PDFBibTeX XMLCite \textit{D. Sármány} et al., J. Sci. Comput. 33, No. 1, 47--74 (2007; Zbl 1128.78014) Full Text: DOI Link
Ruuth, Steven J. Global optimization of explicit strong-stability-preserving Runge-Kutta methods. (English) Zbl 1080.65088 Math. Comput. 75, No. 253, 183-207 (2006). MSC: 65M20 65L06 35L65 PDFBibTeX XMLCite \textit{S. J. Ruuth}, Math. Comput. 75, No. 253, 183--207 (2006; Zbl 1080.65088) Full Text: DOI
Gottlieb, Sigal On high order strong stability preserving Runge-Kutta and multi step time discretizations. (English) Zbl 1203.65166 J. Sci. Comput. 25, No. 1-2, 105-128 (2005). MSC: 65M20 65L06 65L20 PDFBibTeX XMLCite \textit{S. Gottlieb}, J. Sci. Comput. 25, No. 1--2, 105--128 (2005; Zbl 1203.65166) Full Text: DOI
Higueras, Inmaculada Representations of Runge-Kutta methods and strong stability preserving methods. (English) Zbl 1097.65078 SIAM J. Numer. Anal. 43, No. 3, 924-948 (2005). Reviewer: Kai Diethelm (Braunschweig) MSC: 65L06 65L05 65L20 34A34 65L50 PDFBibTeX XMLCite \textit{I. Higueras}, SIAM J. Numer. Anal. 43, No. 3, 924--948 (2005; Zbl 1097.65078) Full Text: DOI
Ketcheson, David I.; Robinson, Allen C. On the practical importance of the SSP property for Runge-Kutta time integrators for some common Godunov-type schemes. (English) Zbl 1071.65121 Int. J. Numer. Methods Fluids 48, No. 3, 271-303 (2005). MSC: 65M06 65L06 65M12 35L65 PDFBibTeX XMLCite \textit{D. I. Ketcheson} and \textit{A. C. Robinson}, Int. J. Numer. Methods Fluids 48, No. 3, 271--303 (2005; Zbl 1071.65121) Full Text: DOI
Ferracina, L.; Spijker, M. N. Stepsize restrictions for the total-variation-diminishing property in general Runge-Kutta methods. (English) Zbl 1080.65087 SIAM J. Numer. Anal. 42, No. 3, 1073-1093 (2004). Reviewer: Angela Handlovičová (Bratislava) MSC: 65M20 65L06 65L05 35L65 65M12 PDFBibTeX XMLCite \textit{L. Ferracina} and \textit{M. N. Spijker}, SIAM J. Numer. Anal. 42, No. 3, 1073--1093 (2004; Zbl 1080.65087) Full Text: DOI
Ruuth, Steven J.; Spiteri, Raymond J. High-order strong-stability-preserving Runge-Kutta methods with downwind-biased spatial discretizations. (English) Zbl 1089.65069 SIAM J. Numer. Anal. 42, No. 3, 974-996 (2004). Reviewer: M. Plum (Karlsruhe) MSC: 65L06 65M20 65L20 34A34 35L65 65M12 65L05 PDFBibTeX XMLCite \textit{S. J. Ruuth} and \textit{R. J. Spiteri}, SIAM J. Numer. Anal. 42, No. 3, 974--996 (2004; Zbl 1089.65069) Full Text: DOI
Pareschi, Lorenzo; Russo, Giovanni High-order asymptotically strong-stability-preserving methods for hyperbolic systems with stiff relaxation. (English) Zbl 1064.65105 Hou, Thomas Y. (ed.) et al., Hyperbolic problems: Theory, numerics, applications. Proceedings of the ninth international conference on hyperbolic problems, Pasadena, CA, USA, March 25–29, 2002. Berlin: Springer (ISBN 3-540-44333-9/hbk). 241-251 (2003). MSC: 65M20 65L06 65M12 35L65 PDFBibTeX XMLCite \textit{L. Pareschi} and \textit{G. Russo}, in: Hyperbolic problems: Theory, numerics, applications. Proceedings of the ninth international conference on hyperbolic problems, Pasadena, CA, USA, March 25--29, 2002. Berlin: Springer. 241--251 (2003; Zbl 1064.65105)
Gottlieb, Sigal; Gottlieb, Lee-Ad J. Strong stability preserving properties of Runge–Kutta time discretization methods for linear constant coefficient operators. (English) Zbl 1030.65099 J. Sci. Comput. 18, No. 1, 83-109 (2003). Reviewer: Angela Handlovičová (Bratislava) MSC: 65M20 65L20 34A30 65M12 65L06 35K15 PDFBibTeX XMLCite \textit{S. Gottlieb} and \textit{L.-A. J. Gottlieb}, J. Sci. Comput. 18, No. 1, 83--109 (2003; Zbl 1030.65099) Full Text: DOI
Spiteri, Raymond J.; Ruuth, Steven J. Non-linear evolution using optimal fourth-order strong-stability-preserving Runge-Kutta methods. (English) Zbl 1015.65031 Math. Comput. Simul. 62, No. 1-2, 125-135 (2003). MSC: 65L06 65L05 65L20 35L60 65L07 34A34 65M20 PDFBibTeX XMLCite \textit{R. J. Spiteri} and \textit{S. J. Ruuth}, Math. Comput. Simul. 62, No. 1--2, 125--135 (2003; Zbl 1015.65031) Full Text: DOI
Spiteri, Raymond J.; Ruuth, Steven J. A new class of optimal high-order strong-stability-preserving time discretization methods. (English) Zbl 1020.65064 SIAM J. Numer. Anal. 40, No. 2, 469-491 (2002). Reviewer: Angela Handlovičová (Bratislava) MSC: 65M20 65L06 65M12 35L70 PDFBibTeX XMLCite \textit{R. J. Spiteri} and \textit{S. J. Ruuth}, SIAM J. Numer. Anal. 40, No. 2, 469--491 (2002; Zbl 1020.65064) Full Text: DOI
Ruuth, Steven J.; Spiteri, Raymond J. Two barriers on strong-stability-preserving time discretization methods. (English) Zbl 1003.65107 J. Sci. Comput. 17, No. 1-4, 211-220 (2002). Reviewer: Erwin Schechter (Kaiserslautern) MSC: 65M20 65M12 35L65 PDFBibTeX XMLCite \textit{S. J. Ruuth} and \textit{R. J. Spiteri}, J. Sci. Comput. 17, No. 1--4, 211--220 (2002; Zbl 1003.65107) Full Text: DOI
Gottlieb, Sigal; Shu, Chi-Wang; Tadmor, Eitan Strong stability-preserving high-order time discretization methods. (English) Zbl 0967.65098 SIAM Rev. 43, No. 1, 89-112 (2001). Reviewer: Michael Sever (Jerusalem) MSC: 65M12 65M20 65-02 65L06 35L65 PDFBibTeX XMLCite \textit{S. Gottlieb} et al., SIAM Rev. 43, No. 1, 89--112 (2001; Zbl 0967.65098) Full Text: DOI