Dzhanunts, G. A.; Romm, Ya. E. The varying piecewise interpolation solution of the Cauchy problem for ordinary differential equations with iterative refinement. (English. Russian original) Zbl 1383.65072 Comput. Math. Math. Phys. 57, No. 10, 1616-1634 (2017); translation from Zh. Vychisl. Mat. Mat. Fiz. 57, No. 10, 1641-1660 (2017). MSC: 65L05 34A34 65L20 65L70 65Y20 65L04 PDF BibTeX XML Cite \textit{G. A. Dzhanunts} and \textit{Ya. E. Romm}, Comput. Math. Math. Phys. 57, No. 10, 1616--1634 (2017; Zbl 1383.65072); translation from Zh. Vychisl. Mat. Mat. Fiz. 57, No. 10, 1641--1660 (2017) Full Text: DOI OpenURL
Nguyen-Ba, Truong; Abdulrahman, Alzahrani; Giordano, Thierry; Vaillancourt, Remi On contractivity-preserving 2- and 3-step predictor-corrector series for ODEs. (English) Zbl 1369.65089 J. Mod. Methods Numer. Math. 8, No. 1-2, 17-39 (2017). MSC: 65L06 65L05 34A34 70F10 PDF BibTeX XML Cite \textit{T. Nguyen-Ba} et al., J. Mod. Methods Numer. Math. 8, No. 1--2, 17--39 (2017; Zbl 1369.65089) Full Text: DOI OpenURL
Soleimani, Behnam; Knoth, Oswald; Weiner, Rüdiger IMEX peer methods for fast-wave-slow-wave problems. (English) Zbl 1367.65111 Appl. Numer. Math. 118, 221-237 (2017). MSC: 65L05 34A34 65L04 86A10 PDF BibTeX XML Cite \textit{B. Soleimani} et al., Appl. Numer. Math. 118, 221--237 (2017; Zbl 1367.65111) Full Text: DOI OpenURL
Luan, Vu Thai Fourth-order two-stage explicit exponential integrators for time-dependent PDEs. (English) Zbl 1354.65143 Appl. Numer. Math. 112, 91-103 (2017). MSC: 65L05 65L06 34A34 65M20 65L04 65L20 PDF BibTeX XML Cite \textit{V. T. Luan}, Appl. Numer. Math. 112, 91--103 (2017; Zbl 1354.65143) Full Text: DOI arXiv OpenURL
Nguyen-Ba, T.; Giordanom, T.; Vaillancourt, R. Contractivity-preserving, 4-step explicit, Hermite-Obrechkoff series ODE solvers of order 3 to 20. (English) Zbl 1374.65123 Acta Univ. Apulensis, Math. Inform. 44, 191-210 (2015). MSC: 65L06 65L05 34A34 65L20 65L70 70F10 PDF BibTeX XML Cite \textit{T. Nguyen-Ba} et al., Acta Univ. Apulensis, Math. Inform. 44, 191--210 (2015; Zbl 1374.65123) OpenURL
Jibunoh, C. C. An exponential method for accurate and automatic integration of nonlinear (stiff and nonstiff) ODE systems. (English) Zbl 1353.65071 J. Niger. Math. Soc. 34, 143-159 (2015). MSC: 65L05 34A34 65L04 65L60 PDF BibTeX XML Cite \textit{C. C. Jibunoh}, J. Niger. Math. Soc. 34, 143--159 (2015; Zbl 1353.65071) Full Text: DOI OpenURL
Niemeyer, Kyle E.; Sung, Chih-Jen GPU-based parallel integration of large numbers of independent ODE systems. (English) Zbl 1317.65157 Kindratenko, Volodymyr (ed.), Numerical computations with GPUs. Cham: Springer (ISBN 978-3-319-06547-2/hbk; 978-3-319-06548-9/ebook). 159-182 (2014). MSC: 65L06 65L05 34A34 65Y05 65L04 PDF BibTeX XML Cite \textit{K. E. Niemeyer} and \textit{C.-J. Sung}, in: Numerical computations with GPUs. Cham: Springer. 159--182 (2014; Zbl 1317.65157) Full Text: DOI arXiv OpenURL
Zhang, Hong; Sandu, Adrian FATODE: a library for forward, adjoint, and tangent linear integration of ODEs. (English) Zbl 1307.65104 SIAM J. Sci. Comput. 36, No. 5, C504-C523 (2014). MSC: 65L05 65L06 65L04 34A34 65Y15 PDF BibTeX XML Cite \textit{H. Zhang} and \textit{A. Sandu}, SIAM J. Sci. Comput. 36, No. 5, C504--C523 (2014; Zbl 1307.65104) Full Text: DOI Link OpenURL
Verner, J. H. Explicit Runge-Kutta pairs with lower stage-order. (English) Zbl 1291.65223 Numer. Algorithms 65, No. 3, 555-577 (2014). MSC: 65L06 65L05 34A34 65L20 65L70 PDF BibTeX XML Cite \textit{J. H. Verner}, Numer. Algorithms 65, No. 3, 555--577 (2014; Zbl 1291.65223) Full Text: DOI OpenURL
Onumanyi, P.; Oladele, J. O.; Adeniyi, R. B.; Awoyemi, D. O. Derivation of finite difference methods by interpolation and collocation. (English) Zbl 1302.65169 Afr. Mat. 24, No. 4, 739-750 (2013). MSC: 65L12 65L05 65L06 65L20 65L60 34A34 PDF BibTeX XML Cite \textit{P. Onumanyi} et al., Afr. Mat. 24, No. 4, 739--750 (2013; Zbl 1302.65169) Full Text: DOI OpenURL
Nguyen-Ba, Truong; Desjardins, Steven J.; Sharp, Philip W.; Vaillancourt, Rémi Contractivity-preserving explicit Hermite-Obrechkoff ODE solver of order 13. (English) Zbl 1284.65087 Celest. Mech. Dyn. Astron. 117, No. 4, 423-434 (2013). MSC: 65L06 65P10 70F10 PDF BibTeX XML Cite \textit{T. Nguyen-Ba} et al., Celest. Mech. Dyn. Astron. 117, No. 4, 423--434 (2013; Zbl 1284.65087) Full Text: DOI OpenURL
Maset, S.; Zennaro, M. Stability properties of explicit exponential Runge-Kutta methods. (English) Zbl 1271.65117 IMA J. Numer. Anal. 33, No. 1, 111-135 (2013). Reviewer: Johannes Schropp (Konstanz) MSC: 65L20 65L06 65L05 34A34 65L04 PDF BibTeX XML Cite \textit{S. Maset} and \textit{M. Zennaro}, IMA J. Numer. Anal. 33, No. 1, 111--135 (2013; Zbl 1271.65117) Full Text: DOI OpenURL
Schmitt, Bernhard A.; Kostina, Ekaterina Peer two-step methods with embedded sensitivity approximation for parameter-dependent ODEs. (English) Zbl 1275.65040 SIAM J. Numer. Anal. 50, No. 5, 2182-2207 (2012). Reviewer: Haydar Akca (Abu Dhabi) MSC: 65L05 34A34 65L04 65L06 65L20 65L50 PDF BibTeX XML Cite \textit{B. A. Schmitt} and \textit{E. Kostina}, SIAM J. Numer. Anal. 50, No. 5, 2182--2207 (2012; Zbl 1275.65040) Full Text: DOI Link OpenURL
Franco, J. M.; Gómez, I. A family of explicit parallel Runge-Kutta-Nyström methods. (English) Zbl 1319.65062 Appl. Math. Comput. 218, No. 8, 4177-4191 (2011). MSC: 65L06 65L05 65Y05 34A34 65L50 PDF BibTeX XML Cite \textit{J. M. Franco} and \textit{I. Gómez}, Appl. Math. Comput. 218, No. 8, 4177--4191 (2011; Zbl 1319.65062) Full Text: DOI OpenURL
Cong, Nguyen Huu; Thuy, Nguyen Thu Two-step-by-two-step PIRK-type PC methods based on Gauss-Legendre collocation points. (English) Zbl 1230.65084 J. Comput. Appl. Math. 236, No. 2, 225-233 (2011). Reviewer: M. Gousidou-Koutita (Thessaloniki) MSC: 65L06 65L05 34A34 65Y05 65L20 PDF BibTeX XML Cite \textit{N. H. Cong} and \textit{N. T. Thuy}, J. Comput. Appl. Math. 236, No. 2, 225--233 (2011; Zbl 1230.65084) Full Text: DOI OpenURL
Cong, Nguyen Huu; Dung, La Tri Twostep-by-twostep continuous PIRKN-type PC methods for nonstiff IVPs. (English) Zbl 1219.65068 Appl. Math. Comput. 217, No. 20, 8010-8019 (2011). MSC: 65L06 65L05 34A34 65L20 65Y05 PDF BibTeX XML Cite \textit{N. H. Cong} and \textit{L. T. Dung}, Appl. Math. Comput. 217, No. 20, 8010--8019 (2011; Zbl 1219.65068) Full Text: DOI OpenURL
Nguyen-Ba, Truong; Bozic, Vladan; Kengne, Emmanuel; Vaillancourt, Rémi A one-step 7-stage Hermite-Birkhoff-Taylor ODE solver of order 11. (English) Zbl 1188.65097 J. Comput. Appl. Math. 234, No. 1, 192-208 (2010). MSC: 65L06 65D05 34A34 65L20 PDF BibTeX XML Cite \textit{T. Nguyen-Ba} et al., J. Comput. Appl. Math. 234, No. 1, 192--208 (2010; Zbl 1188.65097) Full Text: DOI OpenURL
Verner, J. H. Numerically optimal Runge-Kutta pairs with interpolants. (English) Zbl 1184.65074 Numer. Algorithms 53, No. 2-3, 383-396 (2010). MSC: 65L06 65L05 34A34 65L20 65L70 PDF BibTeX XML Cite \textit{J. H. Verner}, Numer. Algorithms 53, No. 2--3, 383--396 (2010; Zbl 1184.65074) Full Text: DOI OpenURL
Schmitt, Bernhard A.; Weiner, Rüdiger Parallel start for explicit parallel two-step peer methods. (English) Zbl 1184.65070 Numer. Algorithms 53, No. 2-3, 363-381 (2010). MSC: 65L05 65Y05 34A34 65L50 PDF BibTeX XML Cite \textit{B. A. Schmitt} and \textit{R. Weiner}, Numer. Algorithms 53, No. 2--3, 363--381 (2010; Zbl 1184.65070) Full Text: DOI OpenURL
Weiner, Rüdiger; Schmitt, Bernhard A.; Podhaisky, Helmut; Jebens, Stefan Superconvergent explicit two-step peer methods. (English) Zbl 1166.65037 J. Comput. Appl. Math. 223, No. 2, 753-764 (2009). Reviewer: M. Gousidou-Koutita (Thessaloniki) MSC: 65L05 65L06 65L20 34A34 PDF BibTeX XML Cite \textit{R. Weiner} et al., J. Comput. Appl. Math. 223, No. 2, 753--764 (2009; Zbl 1166.65037) Full Text: DOI OpenURL
Hoang, Nguyen S.; Sidje, Roger B. Functionally fitted explicit pseudo two-step Runge-Kutta methods. (English) Zbl 1158.65050 Appl. Numer. Math. 59, No. 1, 39-55 (2009). Reviewer: R. Militaru (Craiova) MSC: 65L06 34A34 65L20 65L70 65L50 PDF BibTeX XML Cite \textit{N. S. Hoang} and \textit{R. B. Sidje}, Appl. Numer. Math. 59, No. 1, 39--55 (2009; Zbl 1158.65050) Full Text: DOI OpenURL
Truong, Nguyen-Ba; Kengne, Emmanuel; Vaillancourt, Rémi One-step 4-stage Hermite-Birkhoff-Taylor ODE solver of order 12. (English) Zbl 1168.65366 Can. Appl. Math. Q. 16, No. 1, 77-94 (2008). MSC: 65L05 65L06 34A34 65L20 65L70 PDF BibTeX XML Cite \textit{N.-B. Truong} et al., Can. Appl. Math. Q. 16, No. 1, 77--94 (2008; Zbl 1168.65366) OpenURL
Nguyen-Ba, Truong; Bozic, Vladan; Vaillancourt, Rémi One-step 7-stage Hermite-Birkhoff-Taylor ODE solver of order 13. (English) Zbl 1142.65059 Int. J. Pure Appl. Math. 43, No. 4, 569-592 (2008). MSC: 65L06 65L05 34A34 65L70 65L50 PDF BibTeX XML Cite \textit{T. Nguyen-Ba} et al., Int. J. Pure Appl. Math. 43, No. 4, 569--592 (2008; Zbl 1142.65059) OpenURL
Weiner, Rüdiger; Biermann, Katja; Schmitt, Bernhard A.; Podhaisky, Helmut Explicit two-step peer methods. (English) Zbl 1142.65060 Comput. Math. Appl. 55, No. 4, 609-619 (2008). MSC: 65L06 65L05 34A34 65L20 PDF BibTeX XML Cite \textit{R. Weiner} et al., Comput. Math. Appl. 55, No. 4, 609--619 (2008; Zbl 1142.65060) Full Text: DOI OpenURL
Cong, Nguyen Huu; Xuan, Le Ngoc Improved parallel-iterated pseudo two-step RK methods for nonstiff IVPs. (English) Zbl 1131.65062 Appl. Numer. Math. 58, No. 2, 160-170 (2008). MSC: 65L06 65L05 34A34 65Y05 PDF BibTeX XML Cite \textit{N. H. Cong} and \textit{L. N. Xuan}, Appl. Numer. Math. 58, No. 2, 160--170 (2008; Zbl 1131.65062) Full Text: DOI OpenURL
Nguyen-Ba, Truong; Sharp, Philip W. Hermite-Birkhoff-Obrechkoff 3-stage 4-step ODE solver of order 14 with quantized stepsize. (English) Zbl 1137.65382 Can. Appl. Math. Q. 15, No. 2, 181-202 (2007). MSC: 65L06 65L05 34A34 65L50 65L70 PDF BibTeX XML Cite \textit{T. Nguyen-Ba} and \textit{P. W. Sharp}, Can. Appl. Math. Q. 15, No. 2, 181--202 (2007; Zbl 1137.65382) Full Text: Link OpenURL
Nguyen Cong, Huu; Le Xuan, Ngoc Twostep-by-twostep PIRKC methods. (English) Zbl 1135.65347 Vietnam J. Math. 35, No. 2, 223-229 (2007). MSC: 65L06 65L05 34A34 65Y05 PDF BibTeX XML Cite \textit{H. Nguyen Cong} and \textit{N. Le Xuan}, Vietnam J. Math. 35, No. 2, 223--229 (2007; Zbl 1135.65347) OpenURL
Nguyen Huu Cong; Nguyen Van Minh Continuous parallel-iterated RKN-type PC methods for nonstiff IVPs. (English) Zbl 1141.65057 Appl. Numer. Math. 57, No. 10, 1097-1107 (2007). Reviewer: Thomas Rauber (Bayreuth) MSC: 65L05 65Y05 34A34 65L06 PDF BibTeX XML Cite \textit{Nguyen Huu Cong} and \textit{Nguyen Van Minh}, Appl. Numer. Math. 57, No. 10, 1097--1107 (2007; Zbl 1141.65057) Full Text: DOI OpenURL
Pantano, C. An additive semi-implicit Runge–Kutta family of schemes for nonstiff systems. (English) Zbl 1107.65331 Appl. Numer. Math. 57, No. 3, 297-303 (2007). MSC: 65L06 65L05 34A34 65L20 65M20 35Q53 PDF BibTeX XML Cite \textit{C. Pantano}, Appl. Numer. Math. 57, No. 3, 297--303 (2007; Zbl 1107.65331) Full Text: DOI OpenURL
Cong, N. H.; Podhaisky, H.; Weiner, R. Efficiency of embedded explicit pseudo two-step RKN methods on a shared memory parallel computer. (English) Zbl 1108.65075 Vietnam J. Math. 34, No. 1, 95-108 (2006). MSC: 65L06 65L05 34A34 65Y05 PDF BibTeX XML Cite \textit{N. H. Cong} et al., Vietnam J. Math. 34, No. 1, 95--108 (2006; Zbl 1108.65075) OpenURL
Tirani, Romeo On the minimization of the defect in continuous Runge-Kutta methods. (English) Zbl 1088.65565 Simos, Theodore S. (ed.) et al., ICNAAM 2005. International conference on numerical analysis and applied mathematics 2005. Official conference of the European Society of Computational Methods in Sciences and Engineering (ESCMSE), Rhodes, Greek, September 16–20, 2005. Weinheim: Wiley-VCH (ISBN 3-527-40652-2/hbk). 532-535 (2005). MSC: 65L06 65L05 34A34 PDF BibTeX XML Cite \textit{R. Tirani}, in: ICNAAM 2005. International conference on numerical analysis and applied mathematics 2005. Official conference of the European Society of Computational Methods in Sciences and Engineering (ESCMSE), Rhodes, Greek, September 16--20, 2005. Weinheim: Wiley-VCH. 532--535 (2005; Zbl 1088.65565) OpenURL
Psihoyios, G. Some general formulae for the stability function of explicit advanced step-point (EAS) methods. (English) Zbl 1078.65070 Math. Comput. Modelling 40, No. 11-12, 1171-1179 (2004). Reviewer: Oscar Lopez-Pouso (Santiago de Compostela) MSC: 65L20 65L06 65L05 34A34 PDF BibTeX XML Cite \textit{G. Psihoyios}, Math. Comput. Modelling 40, No. 11--12, 1171--1179 (2004; Zbl 1078.65070) Full Text: DOI OpenURL
Bellen, Alfredo; Zennaro, Marino Adaptive integration of delay differential equations. (English) Zbl 1067.65066 Niculescu, Silviu-Iulian (ed.) et al., Advances in time-delay systems. Berlin: Springer (ISBN 3-540-20890-9/pbk). Lecture Notes in Computational Science and Engineering 38, 155-165 (2004). Reviewer: Alexander O. Ignatyev (Donetsk) MSC: 65L06 65L05 65L70 34K28 PDF BibTeX XML Cite \textit{A. Bellen} and \textit{M. Zennaro}, Lect. Notes Comput. Sci. Eng. 38, 155--165 (2004; Zbl 1067.65066) OpenURL
Nguyen Cong, Huu; Le Xuan, Ngoc Parallel-iterated RK-type PC methods with continuous output formulas. (English) Zbl 1040.65062 Int. J. Comput. Math. 80, No. 8, 1027-1037 (2003). MSC: 65L06 65L05 65Y05 65L20 34A34 PDF BibTeX XML Cite \textit{H. Nguyen Cong} and \textit{N. Le Xuan}, Int. J. Comput. Math. 80, No. 8, 1027--1037 (2003; Zbl 1040.65062) Full Text: DOI OpenURL
Nguyen Huu Cong; Mitsui, Taketomo Parallel predictor-corrector iteration of pseudo two-step RK methods for nonstiff IVPs. (English) Zbl 1026.65055 Japan J. Ind. Appl. Math. 20, No. 1, 51-64 (2003). MSC: 65L06 65L05 65Y05 34A34 PDF BibTeX XML Cite \textit{Nguyen Huu Cong} and \textit{T. Mitsui}, Japan J. Ind. Appl. Math. 20, No. 1, 51--64 (2003; Zbl 1026.65055) Full Text: DOI OpenURL
Franco, J. M. Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators. (English) Zbl 1019.65050 Comput. Phys. Commun. 147, No. 3, 770-787 (2002). Reviewer: Kai Diethelm (Braunschweig) MSC: 65L06 65L20 34A34 65L05 PDF BibTeX XML Cite \textit{J. M. Franco}, Comput. Phys. Commun. 147, No. 3, 770--787 (2002; Zbl 1019.65050) Full Text: DOI OpenURL
Cong, N. H.; Minh, N. T. H. Parallel-iterated pseudo two-step Runge-Kutta-Nyström methods for nonstiff second-order IVPs. (English) Zbl 0999.65067 Comput. Math. Appl. 44, No. 1-2, 143-155 (2002). MSC: 65L06 65L05 65Y05 34A34 PDF BibTeX XML Cite \textit{N. H. Cong} and \textit{N. T. H. Minh}, Comput. Math. Appl. 44, No. 1--2, 143--155 (2002; Zbl 0999.65067) Full Text: DOI OpenURL
Bartoszewski, Zbigniew; Jackiewicz, Zdzisław Toward a two-step Runge-Kutta code for nonstiff differential systems. (English) Zbl 1008.65046 Appl. Math. 28, No. 3, 353-365 (2001). MSC: 65L06 65L05 34A34 65L50 PDF BibTeX XML Cite \textit{Z. Bartoszewski} and \textit{Z. Jackiewicz}, Appl. Math. 28, No. 3, 353--365 (2001; Zbl 1008.65046) Full Text: DOI OpenURL
Nguyen Huu Cong Explicit pseudo two-step RKN methods with stepsize control. (English) Zbl 0983.65087 Appl. Numer. Math. 38, No. 1-2, 135-144 (2001). MSC: 65L06 65L50 34A34 65Y05 65L05 PDF BibTeX XML Cite \textit{Nguyen Huu Cong}, Appl. Numer. Math. 38, No. 1--2, 135--144 (2001; Zbl 0983.65087) Full Text: DOI OpenURL
Cong, Nguyen Huu Continuous variable stepsize explicit pseudo two-step RK methods. (English) Zbl 0947.65085 J. Comput. Appl. Math. 101, No. 1-2, 105-116 (1999). Reviewer: H.Brunner (St.John’s) MSC: 65L06 65L05 65L50 65L70 65Y05 PDF BibTeX XML Cite \textit{N. H. Cong}, J. Comput. Appl. Math. 101, No. 1--2, 105--116 (1999; Zbl 0947.65085) Full Text: DOI OpenURL
Pogorelov, D. Differential-algebraic equations in multibody system modeling. (English) Zbl 0924.70004 Numer. Algorithms 19, No. 1-4, 183-194 (1998). MSC: 70E55 65L05 65L06 PDF BibTeX XML Cite \textit{D. Pogorelov}, Numer. Algorithms 19, No. 1--4, 183--194 (1998; Zbl 0924.70004) Full Text: DOI OpenURL
Shampine, Lawrence F.; Reichelt, Mark W. The MATLAB ODE suite. (English) Zbl 0868.65040 SIAM J. Sci. Comput. 18, No. 1, 1-22 (1997). Reviewer: P.Y.Yalamov (Russe) MSC: 65L05 65L06 34E13 34A34 34-04 65Y15 PDF BibTeX XML Cite \textit{L. F. Shampine} and \textit{M. W. Reichelt}, SIAM J. Sci. Comput. 18, No. 1, 1--22 (1997; Zbl 0868.65040) Full Text: DOI OpenURL
Yaacob, Nazeeruddin; Evans, D. J. A new fifth order explicit Runge-Kutta method with four stages for solving intial value problems in ODEs. (English) Zbl 0891.65087 Int. J. Comput. Math. 65, No. 1-2, 141-147 (1997). Reviewer: V.V.Kobkov (Novosibirsk) MSC: 65L06 34A34 65L20 65L05 65L70 PDF BibTeX XML Cite \textit{N. Yaacob} and \textit{D. J. Evans}, Int. J. Comput. Math. 65, No. 1--2, 141--147 (1997; Zbl 0891.65087) Full Text: DOI OpenURL
Papageorgiou, G.; Tsitouras, Ch. Continuous extensions to high order Runge-Kutta methods. (English) Zbl 0891.65088 Int. J. Comput. Math. 65, No. 3-4, 273-291 (1997). Reviewer: V.V.Kobkov (Novosibirsk) MSC: 65L06 65L05 34A34 65L70 PDF BibTeX XML Cite \textit{G. Papageorgiou} and \textit{Ch. Tsitouras}, Int. J. Comput. Math. 65, No. 3--4, 273--291 (1997; Zbl 0891.65088) Full Text: DOI OpenURL
Frank, J.; Hundsdorfer, W.; Verwer, J. G. On the stability of implicit-explicit linear multistep methods. (English) Zbl 0887.65094 Appl. Numer. Math. 25, No. 2-3, 193-205 (1997). Reviewer: R.Scherer (Karlsruhe) MSC: 65L20 65L06 34A34 34E13 PDF BibTeX XML Cite \textit{J. Frank} et al., Appl. Numer. Math. 25, No. 2--3, 193--205 (1997; Zbl 0887.65094) Full Text: DOI OpenURL
Kappeller, M.; Kiehl, M.; Perzl, M.; Lenke, M. Optimized extrapolation methods for parallel solution of IVPs on different computer architectures. (English) Zbl 0859.65070 Appl. Math. Comput. 77, No. 2-3, 301-315 (1996). Reviewer: T.C.Mohan (Madras) MSC: 65L05 34A34 65Y05 34E13 65L06 PDF BibTeX XML Cite \textit{M. Kappeller} et al., Appl. Math. Comput. 77, No. 2--3, 301--315 (1996; Zbl 0859.65070) Full Text: DOI OpenURL
in’t Hout, Karel J. A note on unconditional maximum norm contractivity of diagonally split Runge-Kutta methods. (English) Zbl 0855.65095 SIAM J. Numer. Anal. 33, No. 3, 1125-1134 (1996). Reviewer: E.Hairer (Genève) MSC: 65L20 65L05 65L06 34A34 PDF BibTeX XML Cite \textit{K. J. in't Hout}, SIAM J. Numer. Anal. 33, No. 3, 1125--1134 (1996; Zbl 0855.65095) Full Text: DOI OpenURL
Rentrop, P.; Strehmel, K.; Weiner, R. A survey of one-step methods for numerical integration in technical simulations. (Ein Überblick über Einschrittverfahren zur numerischen Integration in der technischen Simulation.) (German) Zbl 0849.65051 Mitt. Ges. Angew. Math. Mech. 19, No. 1, 9-43 (1996). Reviewer: E.Hairer (Genève) MSC: 65L06 65-02 65L05 34A09 34A34 80A30 34E13 70F10 PDF BibTeX XML Cite \textit{P. Rentrop} et al., Mitt. Ges. Angew. Math. Mech. 19, No. 1, 9--43 (1996; Zbl 0849.65051) OpenURL
Dormand, John R. Numerical methods for differential equations. A computational approach. Incl. 1 disk. (English) Zbl 0847.65046 CRC Press Library of Engineering Mathematics. Boca Raton, FL: CRC Press. 368 p. (1996). Reviewer: M.Calvo (Zaragoza) MSC: 65L06 65Lxx 65L12 65M20 65L20 65-01 65L05 34A34 34-04 PDF BibTeX XML Cite \textit{J. R. Dormand}, Numerical methods for differential equations. A computational approach. Incl. 1 disk. Boca Raton, FL: CRC Press (1996; Zbl 0847.65046) OpenURL
Ozawa, Kazufumi; Yamada, Susumu Parallel block methods for solving nonstiff equations with stepsize control. (English) Zbl 0933.65083 RIMS Kokyuroku 944, 10-20 (1996). MSC: 65L06 65L05 34A34 65L50 65Y05 65L70 PDF BibTeX XML Cite \textit{K. Ozawa} and \textit{S. Yamada}, RIMS Kokyuroku 944, 10--20 (1996; Zbl 0933.65083) OpenURL
van der Houwen, P. J.; Sommeijer, B. P.; van der Veen, W. A. Parallel iteration across the steps of high-order Runge-Kutta methods for nonstiff initial value problems. (English) Zbl 0837.65077 J. Comput. Appl. Math. 60, No. 3, 309-329 (1995). Reviewer: E.Schechter (Kaiserslautern) MSC: 65L06 65L05 65Y05 34A34 PDF BibTeX XML Cite \textit{P. J. van der Houwen} et al., J. Comput. Appl. Math. 60, No. 3, 309--329 (1995; Zbl 0837.65077) Full Text: DOI OpenURL
Li, Shoufu; Gan, Siqing A class of parallel multistep Runge-Kutta predictor-corrector algorithms. (English. Chinese original) Zbl 0892.65048 Chin. J. Numer. Math. Appl. 17, No. 3, 1-11 (1995); translation from J. Numer. Methods Comput. Appl. 16, No. 1, 7-14 (1995). MSC: 65L06 65Y05 65L20 65L05 34A34 PDF BibTeX XML Cite \textit{S. Li} and \textit{S. Gan}, Chin. J. Numer. Math. Appl. 17, No. 3, 7--14 (1995; Zbl 0892.65048); translation from J. Numer. Methods Comput. Appl. 16, No. 1, 7--14 (1995) OpenURL
Nguyen Huu Cong; Hoang Thi Vi An improvement for explicit parallel Runge-Kutta methods. (English) Zbl 0886.65083 Vietnam J. Math. 23, No. 2, 241-252 (1995). MSC: 65L06 34A34 65L05 65L20 65Y05 PDF BibTeX XML Cite \textit{Nguyen Huu Cong} and \textit{Hoang Thi Vi}, Vietnam J. Math. 23, No. 2, 241--252 (1995; Zbl 0886.65083) OpenURL
Krogh, Fred T. Issues in the design of a multistep code. (English) Zbl 0823.65071 Ann. Numer. Math. 1, No. 1-4, 423-437 (1994). Reviewer: D.Petcu (Timişoara) MSC: 65L06 65L05 34A34 34K05 34E13 PDF BibTeX XML Cite \textit{F. T. Krogh}, Ann. Numer. Math. 1, No. 1--4, 423--437 (1994; Zbl 0823.65071) OpenURL
van der Houwen, P. J.; Sommeijer, B. P. Butcher-Kuntzmann methods for nonstiff problems on parallel computers. (English) Zbl 0812.65064 Appl. Numer. Math. 15, No. 3, 357-374 (1994). Reviewer: W.Schönauer (Karlsruhe) MSC: 65L06 65Y05 65L05 34A34 PDF BibTeX XML Cite \textit{P. J. van der Houwen} and \textit{B. P. Sommeijer}, Appl. Numer. Math. 15, No. 3, 357--374 (1994; Zbl 0812.65064) Full Text: DOI OpenURL
Cong, Nguyen huu Parallel iteration of symmetric Runge-Kutta methods for nonstiff initial-value problems. (English) Zbl 0804.65070 J. Comput. Appl. Math. 51, No. 1, 117-125 (1994). Reviewer: I.N.Katz (St.Louis) MSC: 65L06 65L05 65Y05 34A34 PDF BibTeX XML Cite \textit{N. h. Cong}, J. Comput. Appl. Math. 51, No. 1, 117--125 (1994; Zbl 0804.65070) Full Text: DOI OpenURL
Büttner, Mario; Schmitt, Bernhard A.; Weiner, Rüdiger Automatic partitioning in linearly-implicit Runge-Kutta methods. (English) Zbl 0790.65058 Appl. Numer. Math. 13, No. 1-3, 41-55 (1993). Reviewer: M.M.Konstantinov (Sofia) MSC: 65L05 65L06 34A34 34E13 PDF BibTeX XML Cite \textit{M. Büttner} et al., Appl. Numer. Math. 13, No. 1--3, 41--55 (1993; Zbl 0790.65058) Full Text: DOI OpenURL
Brasey, V.; Hairer, E. Symmetrized half-explicit methods for constrained mechanical systems. (English) Zbl 0787.65043 Appl. Numer. Math. 13, No. 1-3, 23-31 (1993). Reviewer: S.Gocheva-Ilieva (El Menara) MSC: 65L06 65L05 70-08 34A34 PDF BibTeX XML Cite \textit{V. Brasey} and \textit{E. Hairer}, Appl. Numer. Math. 13, No. 1--3, 23--31 (1993; Zbl 0787.65043) Full Text: DOI OpenURL
Hairer, Ernst; Nørsett, Syvert P.; Wanner, Gerhard Solving ordinary differential equations. I: Nonstiff problems. 2. rev. ed. (English) Zbl 0789.65048 Springer Series in Computational Mathematics. 8. Berlin: Springer-Verlag. xv, 528 p. (1993). Reviewer: R.D.Grigorieff (Berlin) MSC: 65L05 65-02 65L20 65Y05 34A30 34A34 65J99 34-01 PDF BibTeX XML Cite \textit{E. Hairer} et al., Solving ordinary differential equations. I: Nonstiff problems. 2. rev. ed. Berlin: Springer-Verlag (1993; Zbl 0789.65048) Full Text: DOI OpenURL
Burrage, Kevin Efficient block predictor-corrector methods with a small number of corrections. (English) Zbl 0782.65088 J. Comput. Appl. Math. 45, No. 1-2, 139-150 (1993). Reviewer: E.Hairer (Genève) MSC: 65L06 65Y05 65L05 34A34 65L60 65L70 PDF BibTeX XML Cite \textit{K. Burrage}, J. Comput. Appl. Math. 45, No. 1--2, 139--150 (1993; Zbl 0782.65088) Full Text: DOI OpenURL
Cash, J. R.; Semnani, S. A new approach to solving nonstiff initial-value problems. (English) Zbl 0782.65089 J. Comput. Appl. Math. 45, No. 1-2, 41-46 (1993). Reviewer: S.Filippi (Gießen) MSC: 65L06 65L05 34A34 PDF BibTeX XML Cite \textit{J. R. Cash} and \textit{S. Semnani}, J. Comput. Appl. Math. 45, No. 1--2, 41--46 (1993; Zbl 0782.65089) Full Text: DOI OpenURL
van der Houwen, P. J. Parallel step-by-step methods. (English) Zbl 0798.65077 Appl. Numer. Math. 11, No. 1-3, 69-81 (1993). Reviewer: Z.Schneider (Bratislava) MSC: 65L05 65Y05 34A34 34E13 PDF BibTeX XML Cite \textit{P. J. van der Houwen}, Appl. Numer. Math. 11, No. 1--3, 69--81 (1993; Zbl 0798.65077) Full Text: DOI OpenURL
Sharp, P. W.; Smart, E. Explicit Runge-Kutta pairs with one more derivative evaluation than the minimum. (English) Zbl 0773.65051 SIAM J. Sci. Comput. 14, No. 2, 338-348 (1993). Reviewer: N.Parhi (Berhampur) MSC: 65L06 65L05 65L20 34A34 PDF BibTeX XML Cite \textit{P. W. Sharp} and \textit{E. Smart}, SIAM J. Sci. Comput. 14, No. 2, 338--348 (1993; Zbl 0773.65051) Full Text: DOI OpenURL
Cash, J. R.; Semnani, S. A modified Adams method for non stiff and mildly stiff initial value problems. (English) Zbl 0889.65084 ACM Trans. Math. Softw. 19, No. 1, 63-80 (1993). MSC: 65L06 65Y20 34A34 34E13 65L05 65L20 PDF BibTeX XML Cite \textit{J. R. Cash} and \textit{S. Semnani}, ACM Trans. Math. Softw. 19, No. 1, 63--80 (1993; Zbl 0889.65084) Full Text: DOI Link OpenURL
Suleiman, Mohamed; Baok, Saiman Using nonconvergence of iteration to partition ODEs. (English) Zbl 0757.65091 Appl. Math. Comput. 49, No. 2-3, 111-140 (1992). Reviewer: Z.Schneider (Bratislava) MSC: 65L06 65L05 34A30 34E13 65L50 PDF BibTeX XML Cite \textit{M. Suleiman} and \textit{S. Baok}, Appl. Math. Comput. 49, No. 2--3, 111--140 (1992; Zbl 0757.65091) Full Text: DOI OpenURL
Berzins, M.; Furzeland, R. M. An adaptive theta method for the solution of stiff and nonstiff differential equations. (English) Zbl 0751.65043 Appl. Numer. Math. 9, No. 1, 1-19 (1992). Reviewer: H.Ade (Mainz) MSC: 65L05 65L50 65L20 34A34 34E13 65M20 PDF BibTeX XML Cite \textit{M. Berzins} and \textit{R. M. Furzeland}, Appl. Numer. Math. 9, No. 1, 1--19 (1992; Zbl 0751.65043) Full Text: DOI OpenURL
Mir, Nazir A.; Masood, M. Farrukh 4 cyclic 4-step \(A\)-stable method. (English) Zbl 0771.65039 J. Math., Punjab Univ. 25, 11-24 (1992). Reviewer: N.Parhi (Berhampur) MSC: 65L06 65L05 65L20 34A34 PDF BibTeX XML Cite \textit{N. A. Mir} and \textit{M. F. Masood}, J. Math., Punjab Univ. 25, 11--24 (1992; Zbl 0771.65039) OpenURL
Tam, H. W. Parallel methods for the numerical solution of ordinary differential equations. (English) Zbl 0767.65058 Computational ordinary differential equations, Proc. Conf., London/UK 1989, Inst. Math. Appl. Conf. Ser., New Ser. 39, 393-404 (1992). Reviewer: D.Petcu (Timişoara) MSC: 65L05 65L20 65Y05 34A34 PDF BibTeX XML Cite \textit{H. W. Tam}, in: Computational ordinary differential equations. Based on the proceedings of a conference, held at Imperial College of Science and Technology, University of London, London, UK, July 3-7, 1989. Oxford: Clarendon Press. 393--404 (1992; Zbl 0767.65058) OpenURL
Sarma, P. A. Families of third, fourth & fifth order extended Nyström methods for \(y'''=f(x,y)\). (English) Zbl 0765.65080 Math., Rev. Anal. Numér. Théor. Approximation, Anal. Numér. Théor. Approximation 20, No. 1-2, 83-95 (1991). Reviewer: E.Schechter (Kaiserslautern) MSC: 65L06 65L05 34A34 PDF BibTeX XML Cite \textit{P. A. Sarma}, Math. Rev. Anal. Numér. Théor. Approximation, Anal. Numér. Théor. Approximation 20, No. 1--2, 83--95 (1991; Zbl 0765.65080) OpenURL
Burrage, Kevin The error behaviour of a general class of predictor-corrector methods. (English) Zbl 0743.65064 Appl. Numer. Math. 8, No. 3, 201-216 (1991). Reviewer: H.R.Schwarz (Zürich) MSC: 65L05 65L70 65L20 34A34 PDF BibTeX XML Cite \textit{K. Burrage}, Appl. Numer. Math. 8, No. 3, 201--216 (1991; Zbl 0743.65064) Full Text: DOI OpenURL
Calvo, M.; Montijano, J. I.; Randez, L. A fifth-order interpolant for the Dormand and Prince Runge-Kutta method. (English) Zbl 0687.65078 J. Comput. Appl. Math. 29, No. 1, 91-100 (1990). Reviewer: A.Coţiu MSC: 65L05 34A34 PDF BibTeX XML Cite \textit{M. Calvo} et al., J. Comput. Appl. Math. 29, No. 1, 91--100 (1990; Zbl 0687.65078) Full Text: DOI OpenURL
van der Houwen, P. J.; Sommeijer, B. P. Parallel iteration of high-order Runge-Kutta methods with stepsize control. (English) Zbl 0682.65039 J. Comput. Appl. Math. 29, No. 1, 111-127 (1990). Reviewer: E.Hairer MSC: 65L05 65L50 34A34 PDF BibTeX XML Cite \textit{P. J. van der Houwen} and \textit{B. P. Sommeijer}, J. Comput. Appl. Math. 29, No. 1, 111--127 (1990; Zbl 0682.65039) Full Text: DOI OpenURL
Randez, L. A new Runge-Kutta method for the resolution of non stiff structured differential equations. (Spanish) Zbl 0711.65055 Differential equations and applications, Proc. 11th Congr., CEDYA, Appl. Math., Fuengirola (Málaga)/Spain 1989, 459-463 (1989). Reviewer: A.de Castro MSC: 65L06 65L05 34A30 PDF BibTeX XML OpenURL
Suleiman, Mohamed bin Solving nonstiff higher order ODEs directly by the direct integration method. (English) Zbl 0689.65047 Appl. Math. Comput. 33, No. 3, 197-219 (1989). Reviewer: R.Jeltsch MSC: 65L05 65L50 34A34 70F05 PDF BibTeX XML Cite \textit{M. b. Suleiman}, Appl. Math. Comput. 33, No. 3, 197--219 (1989; Zbl 0689.65047) Full Text: DOI OpenURL
Higham, Desmond J. Robust defect control with Runge-Kutta schemes. (English) Zbl 0682.65033 SIAM J. Numer. Anal. 26, No. 5, 1175-1183 (1989). Reviewer: M.Bartušek MSC: 65L05 34A34 PDF BibTeX XML Cite \textit{D. J. Higham}, SIAM J. Numer. Anal. 26, No. 5, 1175--1183 (1989; Zbl 0682.65033) Full Text: DOI OpenURL
Higham, Desmond J. Defect estimation in Adams PECE codes. (English) Zbl 0676.65082 SIAM J. Sci. Stat. Comput. 10, No. 5, 964-976 (1989). Reviewer: M.Bartušek MSC: 65L05 34A34 PDF BibTeX XML Cite \textit{D. J. Higham}, SIAM J. Sci. Stat. Comput. 10, No. 5, 964--976 (1989; Zbl 0676.65082) Full Text: DOI OpenURL
Cash, J. R. A block 6(4) Runge-Kutta formula for nonstiff initial value problems. (English) Zbl 0667.65060 ACM Trans. Math. Softw. 15, No. 1, 15-28 (1989). MSC: 65L05 65L20 34A34 PDF BibTeX XML Cite \textit{J. R. Cash}, ACM Trans. Math. Softw. 15, No. 1, 15--28 (1989; Zbl 0667.65060) Full Text: DOI Link OpenURL
Kal’yanova, N. L.; Zakharov, A. Yu.; Markachev, Yu. E. LSODA - a packet of programs for the numerical solution of stiff and nonstiff systems of ordinary differential equations with an automatic choice of integration. Instructions. (LSODA - paket programm dlya chislennogo resheniya zhestkikh i nezhestkikh sistem obyknovennykh differentsial\(\{\) nykh uravnenij s avtomaticheskim vyborom metoda integrirovaniya). (Russian) Zbl 0668.65052 Moskva: AN SSSR. Institut Prikladnoj Matematiki Im. M. V. Keldysha. 32 p. R. 0.15 (1988). Reviewer: G.Dimitriu MSC: 65L05 34-04 34A34 PDF BibTeX XML OpenURL
Bruder, Jürgen; Strehmel, Karl; Weiner, Rüdiger Partitioned adaptive Runge-Kutta methods for the solution of nonstiff and stiff systems. (English) Zbl 0655.65095 Numer. Math. 52, No. 6, 621-638 (1988). Reviewer: R.Jeltsch MSC: 65L05 65L50 34A34 PDF BibTeX XML Cite \textit{J. Bruder} et al., Numer. Math. 52, No. 6, 621--638 (1988; Zbl 0655.65095) Full Text: DOI EuDML OpenURL
Szyszkowicz, M. Two one-step methods to solve the initial value problem. (English) Zbl 0642.65054 Zastosow. Mat. 19, 149-156 (1987). Reviewer: K.Burrage MSC: 65L05 65L50 34A34 34-04 PDF BibTeX XML Cite \textit{M. Szyszkowicz}, Zastosow. Mat. 19, 149--156 (1987; Zbl 0642.65054) OpenURL
Hairer, Ernst; Nørsett, Syvert P.; Wanner, Gerhard Solving ordinary differential equations. I: Nonstiff problems. (English) Zbl 0638.65058 Springer Series in Computational Mathematics, 8. Berlin etc.: Springer- Verlag XIII, 480 p.; DM 124.00 (1987). Reviewer: R.D.Grigorieff MSC: 65L05 65-02 65L20 34A30 34A34 65J99 34A12 34-01 PDF BibTeX XML OpenURL
Hall, George Equilibrium states of Runge-Kutta schemes. II. (English) Zbl 0633.65062 ACM Trans. Math. Softw. 12, 183-192 (1986). Reviewer: H.Ade MSC: 65L05 65L20 65L50 34A34 PDF BibTeX XML Cite \textit{G. Hall}, ACM Trans. Math. Softw. 12, 183--192 (1986; Zbl 0633.65062) Full Text: DOI Link OpenURL
Ascher, Uri Collocation for two-point boundary value problems revisited. (English) Zbl 0618.65072 SIAM J. Numer. Anal. 23, 596-609 (1986). Reviewer: T.Mitsui MSC: 65L10 65L20 34B15 PDF BibTeX XML Cite \textit{U. Ascher}, SIAM J. Numer. Anal. 23, 596--609 (1986; Zbl 0618.65072) Full Text: DOI OpenURL
Day, J. D. A minimum configuration fourth-order nonautonomous explicit Rosenbrock method for nonstiff differential equations. (English) Zbl 0596.65043 J. Comput. Appl. Math. 16, 247-250 (1986). MSC: 65L05 34A34 PDF BibTeX XML Cite \textit{J. D. Day}, J. Comput. Appl. Math. 16, 247--250 (1986; Zbl 0596.65043) Full Text: DOI OpenURL
Rentrop, Peter Partitioned Runge-Kutta methods with stiffness detection and stepsize control. (English) Zbl 0625.65059 Numer. Math. 47, 545-564 (1985). Reviewer: K.Burrage MSC: 65L05 65L20 65L50 34A34 PDF BibTeX XML Cite \textit{P. Rentrop}, Numer. Math. 47, 545--564 (1985; Zbl 0625.65059) Full Text: DOI EuDML OpenURL
Hall, G.; Suleiman, M. B. A single code for the solution of stiff and nonstiff ODE’s. (English) Zbl 0601.65055 SIAM J. Sci. Stat. Comput. 6, 684-697 (1985). Reviewer: H.Ade MSC: 65L05 65L20 34A34 PDF BibTeX XML Cite \textit{G. Hall} and \textit{M. B. Suleiman}, SIAM J. Sci. Stat. Comput. 6, 684--697 (1985; Zbl 0601.65055) Full Text: DOI OpenURL
Cash, J. R. Block Runge-Kutta methods for the numerical integration of initial value problems in ordinary differential equations. I: The nonstiff case. (English) Zbl 0529.65043 Math. Comput. 40, 175-191 (1983). MSC: 65L05 PDF BibTeX XML Cite \textit{J. R. Cash}, Math. Comput. 40, 175--191 (1983; Zbl 0529.65043) Full Text: DOI OpenURL
Petzold, Linda Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations. (English) Zbl 0518.65051 SIAM J. Sci. Stat. Comput. 4, 136-148 (1983). MSC: 65L05 65Y99 PDF BibTeX XML Cite \textit{L. Petzold}, SIAM J. Sci. Stat. Comput. 4, 136--148 (1983; Zbl 0518.65051) Full Text: DOI OpenURL
Hanson, P. M.; Enright, W. H. Controlling the defect in existing variable-order Adams codes for initial-value problems. (English) Zbl 0508.65033 ACM Trans. Math. Softw. 9, 71-97 (1983). MSC: 65L05 PDF BibTeX XML Cite \textit{P. M. Hanson} and \textit{W. H. Enright}, ACM Trans. Math. Softw. 9, 71--97 (1983; Zbl 0508.65033) Full Text: DOI OpenURL
Carver, M. B.; MacEwen, S. R. On the use of sparse matrix approximation to the Jacobian in integrating large sets of ordinary differential equations. (English) Zbl 0477.65054 SIAM J. Sci. Stat. Comput. 2, 51-64 (1981). MSC: 65L05 PDF BibTeX XML Cite \textit{M. B. Carver} and \textit{S. R. MacEwen}, SIAM J. Sci. Stat. Comput. 2, 51--64 (1981; Zbl 0477.65054) Full Text: DOI OpenURL
Gomm, W. Stability analysis of explicit multirate methods. (English) Zbl 0469.65052 Math. Comput. Simulation 23, 34-50 (1981). MSC: 65L05 65L20 PDF BibTeX XML Cite \textit{W. Gomm}, Math. Comput. Simul. 23, 34--50 (1981; Zbl 0469.65052) Full Text: DOI OpenURL
Jackson, K. R.; Enright, W. H.; Hull, T. E. A theoretical criterion for comparing Runge-Kutta formulas. (English) Zbl 0391.65030 SIAM J. Numer. Anal. 15, 618-641 (1978). MSC: 65L05 PDF BibTeX XML Cite \textit{K. R. Jackson} et al., SIAM J. Numer. Anal. 15, 618--641 (1978; Zbl 0391.65030) Full Text: DOI OpenURL