Li, Shishun; Wang, Jing-Yuan; Cai, Xiao-Chuan \(A\)-stable high-order block implicit methods for parabolic equations. (English) Zbl 1520.65053 SIAM J. Numer. Anal. 61, No. 4, 1858-1884 (2023). MSC: 65L05 65L20 65M55 65M60 PDFBibTeX XMLCite \textit{S. Li} et al., SIAM J. Numer. Anal. 61, No. 4, 1858--1884 (2023; Zbl 1520.65053) Full Text: DOI
Givoli, Dan Dahlquist’s barriers and much beyond. (English) Zbl 07649260 J. Comput. Phys. 475, Article ID 111836, 19 p. (2023). MSC: 65Lxx 65Mxx 34Axx PDFBibTeX XMLCite \textit{D. Givoli}, J. Comput. Phys. 475, Article ID 111836, 19 p. (2023; Zbl 07649260) Full Text: DOI
Shi, Wenjie; Tartakovsky, Daniel M. Polynomial chaos expansions for stiff random ODEs. (English) Zbl 1492.65017 SIAM J. Sci. Comput. 44, No. 3, A1021-A1046 (2022). MSC: 65C20 65C30 60H35 65L04 65L06 PDFBibTeX XMLCite \textit{W. Shi} and \textit{D. M. Tartakovsky}, SIAM J. Sci. Comput. 44, No. 3, A1021--A1046 (2022; Zbl 1492.65017) Full Text: DOI
Olatunji, P. O.; Ikhile, M. N. O.; Okuonghae, R. I. Nested second derivative two-step Runge-Kutta methods. (English) Zbl 1499.65288 Int. J. Appl. Comput. Math. 7, No. 6, Paper No. 249, 39 p. (2021). MSC: 65L05 65L06 PDFBibTeX XMLCite \textit{P. O. Olatunji} et al., Int. J. Appl. Comput. Math. 7, No. 6, Paper No. 249, 39 p. (2021; Zbl 1499.65288) Full Text: DOI
Lang, Jens Rosenbrock-Wanner methods: construction and mission. (English) Zbl 1477.65008 Jax, Tim (ed.) et al., Rosenbrock-Wanner-type methods. Theory and applications. Based on the minisymposium, University of Bath, Bath, UK, September 2017. Cham: Springer. Math. Online First Collect., 1-17 (2021). MSC: 65-03 PDFBibTeX XMLCite \textit{J. Lang}, in: Rosenbrock-Wanner-type methods. Theory and applications. Based on the minisymposium, University of Bath, Bath, UK, September 2017. Cham: Springer. 1--17 (2021; Zbl 1477.65008) Full Text: DOI arXiv
Akrivis, Georgios; Katsoprinakis, Emmanouil An analogue to the a \((\vartheta)\)-stability concept for implicit-explicit BDF methods. (English) Zbl 1457.65031 SIAM J. Numer. Anal. 58, No. 6, 3475-3503 (2020). MSC: 65L06 65L20 65L04 PDFBibTeX XMLCite \textit{G. Akrivis} and \textit{E. Katsoprinakis}, SIAM J. Numer. Anal. 58, No. 6, 3475--3503 (2020; Zbl 1457.65031) Full Text: DOI
Akrivis, Georgios; Katsoprinakis, Emmanouil Maximum angles of \(\mathrm{A}(\vartheta)\)-stability of backward difference formulae. (English) Zbl 1431.65104 BIT 60, No. 1, 93-99 (2020). MSC: 65L06 65L20 65L04 PDFBibTeX XMLCite \textit{G. Akrivis} and \textit{E. Katsoprinakis}, BIT 60, No. 1, 93--99 (2020; Zbl 1431.65104) Full Text: DOI
Li, Bowen; Ding, Jieyu; Li, Yanan L-stable method for differential-algebraic equations of multibody system dynamics. (English) Zbl 1435.65114 Math. Probl. Eng. 2019, Article ID 9283461, 11 p. (2019). MSC: 65L80 70E55 PDFBibTeX XMLCite \textit{B. Li} et al., Math. Probl. Eng. 2019, Article ID 9283461, 11 p. (2019; Zbl 1435.65114) Full Text: DOI
Zhao, Jiaxin; Wang, Hongwei; Zhang, Heming An accurate method for real-time aircraft dynamics simulation based on predictor-corrector scheme. (English) Zbl 1394.76094 Math. Probl. Eng. 2015, Article ID 193179, 10 p. (2015). MSC: 76M25 76G25 PDFBibTeX XMLCite \textit{J. Zhao} et al., Math. Probl. Eng. 2015, Article ID 193179, 10 p. (2015; Zbl 1394.76094) Full Text: DOI
Grimich, K.; Michel, B.; Cinnella, P.; Lerat, A. An accurate finite-volume formulation of a residual-based compact scheme for unsteady compressible flows. (English) Zbl 1391.76412 Comput. Fluids 92, 93-112 (2014). MSC: 76M12 65M08 PDFBibTeX XMLCite \textit{K. Grimich} et al., Comput. Fluids 92, 93--112 (2014; Zbl 1391.76412) Full Text: DOI
Lerat, A.; Grimich, K.; Cinnella, P. On the design of high order residual-based dissipation for unsteady compressible flows. (English) Zbl 1291.76246 J. Comput. Phys. 235, 32-51 (2013). MSC: 76M25 76N99 35L65 PDFBibTeX XMLCite \textit{A. Lerat} et al., J. Comput. Phys. 235, 32--51 (2013; Zbl 1291.76246) Full Text: DOI
Okuonghae, R. I.; Ikhile, M. N. O. The numerical solution of stiff IVPs in ODEs using modified second derivative BDF. (English) Zbl 1273.65099 Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 51, No. 1, 51-77 (2012). MSC: 65L05 65L04 34A34 65L06 65L20 PDFBibTeX XMLCite \textit{R. I. Okuonghae} and \textit{M. N. O. Ikhile}, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 51, No. 1, 51--77 (2012; Zbl 1273.65099) Full Text: Link
Okuonghae, R. I.; Ikhile, M. N. O. A \((\alpha)\)-stable linear multistep methods for stiff IVPs in ODEs. (English) Zbl 1244.65098 Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 50, No. 1, 73-90 (2011). MSC: 65L04 65L05 65L06 PDFBibTeX XMLCite \textit{R. I. Okuonghae} and \textit{M. N. O. Ikhile}, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 50, No. 1, 73--90 (2011; Zbl 1244.65098) Full Text: EuDML
Layton, Anita T.; Minion, Michael L. Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. (English) Zbl 1078.65552 BIT 45, No. 2, 341-373 (2005). MSC: 65L05 34A34 65L20 65L50 PDFBibTeX XMLCite \textit{A. T. Layton} and \textit{M. L. Minion}, BIT 45, No. 2, 341--373 (2005; Zbl 1078.65552) Full Text: DOI Link
Zhang, C. J.; Zhou, S. Z. Stability analysis of LMMs for systems of neutral multidelay-differential equations. (English) Zbl 0940.65085 Comput. Math. Appl. 38, No. 3-4, 113-117 (1999). Reviewer: N.Parhi (Berhampur) MSC: 65L20 34K28 34K40 65L07 65L06 PDFBibTeX XMLCite \textit{C. J. Zhang} and \textit{S. Z. Zhou}, Comput. Math. Appl. 38, No. 3--4, 113--117 (1999; Zbl 0940.65085) Full Text: DOI
Savaré, Giuseppe \(A(\Theta)\)-stable approximation of abstract Cauchy problems. (English) Zbl 0791.65077 Numer. Math. 65, No. 3, 319-335 (1993). Reviewer: G.Savaré (Pavia) MSC: 65M60 65M12 65J10 35G10 35K25 34G10 PDFBibTeX XMLCite \textit{G. Savaré}, Numer. Math. 65, No. 3, 319--335 (1993; Zbl 0791.65077) Full Text: DOI EuDML
Auzinger, W.; Frank, R.; Kirlinger, G. Modern convergence theory for stiff initial-value problems. (English) Zbl 0782.65087 J. Comput. Appl. Math. 45, No. 1-2, 5-16 (1993). Reviewer: E.Hairer (Genève) MSC: 65L06 65L20 65L05 34E13 34A34 PDFBibTeX XMLCite \textit{W. Auzinger} et al., J. Comput. Appl. Math. 45, No. 1--2, 5--16 (1993; Zbl 0782.65087) Full Text: DOI
Chan, R. P. K. Generalized symmetric Runge-Kutta methods. (English) Zbl 0773.65047 Computing 50, No. 1, 31-49 (1993). Reviewer: R.Lamour (Berlin) MSC: 65L06 65L05 65L20 34A34 34E13 PDFBibTeX XMLCite \textit{R. P. K. Chan}, Computing 50, No. 1, 31--49 (1993; Zbl 0773.65047) Full Text: DOI
Savaré, G. A \(\Theta\)-stable discretization of abstract differential equations. (Italian. English summary) Zbl 0762.65053 Calcolo 28, No. 3-4, 205-247 (1991). Reviewer: E.V.Nicolau (Bucureşti) MSC: 65M20 65M12 65L05 35G10 35K25 PDFBibTeX XMLCite \textit{G. Savaré}, Calcolo 28, No. 3--4, 205--247 (1991; Zbl 0762.65053) Full Text: DOI
Chakravarti, P. C.; Kamel, M. S. High order formulas with second derivatives for the numerical integration of stiff ordinary differential equations. (English) Zbl 0704.65059 Int. J. Comput. Math. 34, No. 1-2, 95-104 (1990). Reviewer: E.Hairer MSC: 65L20 65L05 34A34 PDFBibTeX XMLCite \textit{P. C. Chakravarti} and \textit{M. S. Kamel}, Int. J. Comput. Math. 34, No. 1--2, 95--104 (1990; Zbl 0704.65059) Full Text: DOI
Urbani, A. M. Modified ROW methods for stiff problems. (Italian. English summary) Zbl 0747.65063 Calcolo 27, No. 1-2, 89-102 (1990). Reviewer: M.Calvo (Zaragoza) MSC: 65L06 65L20 65L05 34A34 34E13 PDFBibTeX XMLCite \textit{A. M. Urbani}, Calcolo 27, No. 1--2, 89--102 (1990; Zbl 0747.65063) Full Text: DOI
Bertoluzza, S. Discretization of parabolic inequalities. (English) Zbl 0712.65064 Calcolo 26, No. 2-4, 237-266 (1989). Reviewer: W.H.Schmidt MSC: 65K10 35K85 49J40 PDFBibTeX XMLCite \textit{S. Bertoluzza}, Calcolo 26, No. 2--4, 237--266 (1989; Zbl 0712.65064) Full Text: DOI
Butcher, J. C.; Cash, J. R. Some recent developments on numerical initial value problems: A survey. (English) Zbl 0676.65090 Appl. Numer. Math. 5, No. 1-2, 3-18 (1989). Reviewer: J.H.Verner MSC: 65L20 65L05 65-02 34A34 PDFBibTeX XMLCite \textit{J. C. Butcher} and \textit{J. R. Cash}, Appl. Numer. Math. 5, No. 1--2, 3--18 (1989; Zbl 0676.65090) Full Text: DOI
Rockswold, Gary K. \(A_ 0\)-stable linear multistep formulas of the \(\alpha\)-type. (English) Zbl 0626.65070 BIT 27, 123-128 (1987). Reviewer: K.Burrage MSC: 65L05 65L20 34A34 PDFBibTeX XMLCite \textit{G. K. Rockswold}, BIT 27, 123--128 (1987; Zbl 0626.65070) Full Text: DOI
Jeltsch, Rolf; Nevanlinna, Olavi Accuracy and stability of multistage multistep formulas. (English) Zbl 0563.65049 Numer. Math. 48, 33-83 (1986). MSC: 65L05 65L20 PDFBibTeX XMLCite \textit{R. Jeltsch} and \textit{O. Nevanlinna}, Numer. Math. 48, 33--83 (1986; Zbl 0563.65049) Full Text: DOI EuDML
Jeltsch, Rolf; Nevanlinna, Olavi Dahlquist’s first barrier for multistage multistep formulas. (English) Zbl 0562.65049 BIT 24, 538-555 (1984). Reviewer: M.Reimer MSC: 65L05 65L20 PDFBibTeX XMLCite \textit{R. Jeltsch} and \textit{O. Nevanlinna}, BIT 24, 538--555 (1984; Zbl 0562.65049) Full Text: DOI
Chakravarti, P. C.; Kamel, M. S. Stiffly stable second derivative multistep methods with higher order and improved stability regions. (English) Zbl 0507.65034 BIT 23, 75-83 (1983). MSC: 65L05 65L20 PDFBibTeX XMLCite \textit{P. C. Chakravarti} and \textit{M. S. Kamel}, BIT 23, 75--83 (1983; Zbl 0507.65034) Full Text: DOI
Watanabe, Kajiro; Himmelblau, David M. Analysis of trajectory errors in integrating ordinary differential equations. (English) Zbl 0503.65051 J. Franklin Inst. 314, 283-321 (1982). MSC: 65L05 65L20 PDFBibTeX XMLCite \textit{K. Watanabe} and \textit{D. M. Himmelblau}, J. Franklin Inst. 314, 283--321 (1982; Zbl 0503.65051) Full Text: DOI
Jeltsch, Rolf; Nevanlinna, Olavi Stability and accuracy of time discretizations for initial value problems. (English) Zbl 0493.65038 Numer. Math. 40, 245-296 (1982). MSC: 65L20 65L05 PDFBibTeX XMLCite \textit{R. Jeltsch} and \textit{O. Nevanlinna}, Numer. Math. 40, 245--296 (1982; Zbl 0493.65038) Full Text: DOI EuDML
Miranker, W. L.; Chern, I-L. Dichotomy and conjugate gradients in the stiff initial value problem. (English) Zbl 0488.65026 Linear Algebra Appl. 36, 57-77 (1981). MSC: 65L05 65F10 PDFBibTeX XMLCite \textit{W. L. Miranker} and \textit{I-L. Chern}, Linear Algebra Appl. 36, 57--77 (1981; Zbl 0488.65026) Full Text: DOI
Bui, Tien D. Solving stiff differential equations in the simulation of physical systems. (English) Zbl 0471.65048 Simulation 37, 37-46 (1981). MSC: 65L05 65C20 68U20 PDFBibTeX XML Full Text: DOI
Grigorieff, R. D.; Schroll, J. Über \(A(\alpha)\)-stabile Verfahren hoher Konsistenzordnung. (German) Zbl 0395.65043 Computing 20, 343-350 (1978). MSC: 65L07 65L05 PDFBibTeX XMLCite \textit{R. D. Grigorieff} and \textit{J. Schroll}, Computing 20, 343--350 (1978; Zbl 0395.65043) Full Text: DOI
Moore, P. Orbitally stable multistep methods. (English) Zbl 0388.65034 Celestial Mech. 17, 281-297 (1978). MSC: 65L07 65L05 70F15 70M20 PDFBibTeX XMLCite \textit{P. Moore}, Celest. Mech. 17, 281--297 (1978; Zbl 0388.65034) Full Text: DOI
Bickart, T. A.; Jury, E. I. Arithmetic tests for \(A\)-stability, \(A[\alpha]\)-stability, and stiff- stability. (English) Zbl 0382.65035 BIT, Nord. Tidskr. Inf.-behandl. 18, 9-21 (1978). MSC: 65L07 65L05 PDFBibTeX XMLCite \textit{T. A. Bickart} and \textit{E. I. Jury}, BIT, Nord. Tidskr. Inf.-behandl. 18, 9--21 (1978; Zbl 0382.65035) Full Text: DOI
Kobza, Jiri Stability of the second derivative linear multistep formulas. (English) Zbl 0396.65044 Acta Univ. Palack. Olomuc., Fac. Rer. Natur. 53, Math. 16, 167-184 (1977). MSC: 65L07 65L05 PDFBibTeX XMLCite \textit{J. Kobza}, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 16, 167--184 (1977; Zbl 0396.65044) Full Text: EuDML
Alfeld, P.; Lambert, J. D. Correction in the dominant space: A numerical technique for a certain class of stiff initial value problems. (English) Zbl 0391.65031 Math. Comput. 31, 922-938 (1977). MSC: 65L05 PDFBibTeX XMLCite \textit{P. Alfeld} and \textit{J. D. Lambert}, Math. Comput. 31, 922--938 (1977; Zbl 0391.65031) Full Text: DOI
Odeh, F.; Liniger, W. Nonlinear fixed-h stability of linear multistep formulas. (English) Zbl 0378.65041 J. Math. Anal. Appl. 61, 691-712 (1977). MSC: 65L05 PDFBibTeX XMLCite \textit{F. Odeh} and \textit{W. Liniger}, J. Math. Anal. Appl. 61, 691--712 (1977; Zbl 0378.65041) Full Text: DOI
von Welck, U. Stabile Mehrschichtverfahren für parabolische Evolutionsgleichungen. (German) Zbl 0351.65021 Numer. Math. 29, 65-82 (1977). MSC: 65M15 65M06 65M12 35K10 PDFBibTeX XMLCite \textit{U. von Welck}, Numer. Math. 29, 65--82 (1977; Zbl 0351.65021) Full Text: DOI EuDML
Jeltsch, Rolf Multistep methods using higher derivatives and damping at infinity. (English) Zbl 0348.65071 Math. Comput. 31, 124-138 (1977). MSC: 65L05 PDFBibTeX XMLCite \textit{R. Jeltsch}, Math. Comput. 31, 124--138 (1977; Zbl 0348.65071) Full Text: DOI
Hennart, J. P. One-step piecewise polynomial multiple collocation methods for initial value problems. (English) Zbl 0348.65068 Math. Comput. 31, 24-36 (1977). MSC: 65L05 65J99 PDFBibTeX XMLCite \textit{J. P. Hennart}, Math. Comput. 31, 24--36 (1977; Zbl 0348.65068) Full Text: DOI
Gupta, G. K. Some new high-order multistep formulae for solving stiff equations. (English) Zbl 0332.65046 Math. Comput. 30, 417-432 (1976). MSC: 65L05 65D30 PDFBibTeX XMLCite \textit{G. K. Gupta}, Math. Comput. 30, 417--432 (1976; Zbl 0332.65046) Full Text: DOI
Matthys, J. A-stable linear multistep methods for Volterra integro-differential equations. (English) Zbl 0319.65072 Numer. Math. 27, 85-94 (1976). MSC: 65R20 45K05 PDFBibTeX XMLCite \textit{J. Matthys}, Numer. Math. 27, 85--94 (1976; Zbl 0319.65072) Full Text: DOI EuDML
Fuchs, F. A-stability of Runge-Kutta methods with single and multiple nodes. (English) Zbl 0316.65012 Computing 16, 39-48 (1976). MSC: 65L05 65J99 PDFBibTeX XMLCite \textit{F. Fuchs}, Computing 16, 39--48 (1976; Zbl 0316.65012) Full Text: DOI
Gupta, G. K.; Wallace, C. S. Some new multistep methods for solving ordinary differential equations. (English) Zbl 0302.65058 Math. Comput. 29, 489-500 (1975). MSC: 65L05 65D30 PDFBibTeX XMLCite \textit{G. K. Gupta} and \textit{C. S. Wallace}, Math. Comput. 29, 489--500 (1975; Zbl 0302.65058) Full Text: DOI
Prothero, A.; Robinson, A. On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations. (English) Zbl 0309.65034 Math. Comput. 28, 145-162 (1974). MSC: 65L05 65J99 34D05 34E05 PDFBibTeX XMLCite \textit{A. Prothero} and \textit{A. Robinson}, Math. Comput. 28, 145--162 (1974; Zbl 0309.65034) Full Text: DOI
Sarkany, E. F.; Liniger, W. Exponential fitting of matricial multistep methods for ordinary differential equations. (English) Zbl 0293.65049 Math. Comput. 28, 1035-1052 (1974). MSC: 65L05 65D30 39B42 PDFBibTeX XMLCite \textit{E. F. Sarkany} and \textit{W. Liniger}, Math. Comput. 28, 1035--1052 (1974; Zbl 0293.65049) Full Text: DOI
Axelsson, O. On the efficiency of a class of \(A\)-stable methods. (English) Zbl 0289.65028 BIT, Nord. Tidskr. Inf.-behandl. 14, 279-287 (1974). MSC: 65L05 PDFBibTeX XMLCite \textit{O. Axelsson}, BIT, Nord. Tidskr. Inf.-behandl. 14, 279--287 (1974; Zbl 0289.65028) Full Text: DOI
Bickart, Theodore A.; Picel, Zdenek High order stiffly stable composite multistep methods for numerical integration of stiff differential equations. (English) Zbl 0265.65040 BIT, Nord. Tidskr. Inf.-behandl. 13, 272-286 (1973). MSC: 65L05 PDFBibTeX XMLCite \textit{T. A. Bickart} and \textit{Z. Picel}, BIT, Nord. Tidskr. Inf.-behandl. 13, 272--286 (1973; Zbl 0265.65040) Full Text: DOI
Cryer, Colin W. A new class of highly-stable methods: A\(_0\)-stable methods. (English) Zbl 0265.65036 BIT, Nord. Tidskr. Inf.-behandl. 13, 153-159 (1973). MSC: 65L05 PDFBibTeX XMLCite \textit{C. W. Cryer}, BIT, Nord. Tidskr. Inf.-behandl. 13, 153--159 (1973; Zbl 0265.65036) Full Text: DOI
Odeh, F.; Liniger, W. A note on unconditional fixed-h stability of linear multistep formulae. (English) Zbl 0221.65124 Computing 7, 240-253 (1971). MSC: 65L06 30F30 65L07 PDFBibTeX XMLCite \textit{F. Odeh} and \textit{W. Liniger}, Computing 7, 240--253 (1971; Zbl 0221.65124) Full Text: DOI
Axelsson, O. A class of \(A\)-stable methods. (English) Zbl 0208.41504 BIT, Nord. Tidskr. Inf.-behandl. 9, 185-190 (1969). MSC: 65L05 65L20 PDFBibTeX XMLCite \textit{O. Axelsson}, BIT, Nord. Tidskr. Inf.-behandl. 9, 185--190 (1969; Zbl 0208.41504) Full Text: DOI
Nørsett, Syvert P. A criterion for \(A(\alpha)\)-stability of linear multistep methods. (English) Zbl 0185.41701 BIT, Nord. Tidskr. Inf.-behandl. 9, 259-263 (1969). PDFBibTeX XMLCite \textit{S. P. Nørsett}, BIT, Nord. Tidskr. Inf.-behandl. 9, 259--263 (1969; Zbl 0185.41701) Full Text: DOI