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Dahlquist, Germund (b. 1925 d. 2005)

Author ID: dahlquist.germund-g Recent zbMATH articles by "Dahlquist, Germund"
Published as: Dahlquist, Germund; Dahlquist, G.; Dahlquist, Germund G.; Dahlquist, G. G.
External Links: MacTutor · MGP · Wikidata · dblp · GND · IdRef
Documents Indexed: 56 Publications since 1951, including 14 Books
1 Contribution as Editor
Biographic References: 1 Publication
Co-Authors: 28 Co-Authors with 23 Joint Publications
744 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

49 Publications have been cited 1,618 times in 1,281 Documents Cited by Year
A special stability problem for linear multistep methods. Zbl 0123.11703
Dahlquist, Germund G.
454
1963
Convergence and stability in the numerical integration of ordinary differential equations. Zbl 0071.11803
Dahlquist, Germund
168
1956
Numerical methods in scientific computing. Vol. 1. Zbl 1153.65001
Dahlquist, Germund; Björck, Åke
152
2008
Stability and error bounds in the numerical integration of ordinary differential equations. Zbl 0085.33401
Dahlquist, Germund
148
1959
G-stability is equivalent to A-stability. Zbl 0413.65057
Dahlquist, Germund
114
1978
Error analysis for a class of methods for stiff non-linear initial value problems. Zbl 0352.65042
Dahlquist, Germund
86
1976
On accuracy and unconditional stability of linear multistep methods for second order differential equations. Zbl 0378.65043
Dahlquist, Germund
75
1978
Reducibility and contractivity of Runge-Kutta methods revisited. Zbl 1106.65062
Dahlquist, Germund; Jeltsch, Rolf
39
2006
Numerical methods. Translated from the Swedish by Ned Anderson. Reprint of the 1974 English translation. Zbl 1029.65002
Dahlquist, Germund; Björck, Åke
32
2003
Stability of two-step methods for variable integration steps. Zbl 0526.65049
Dahlquist, Germund G.; Liniger, Werner; Nevanlinna, Olavi
32
1983
Problems related to the numerical treatment of stiff differential equations. Zbl 0275.65023
Dahlquist, Germund
28
1974
On one-leg multistep methods. Zbl 0529.65048
Dahlquist, Germund
23
1983
Bounds for the error of linear systems of equations using the theory of moments. Zbl 0238.65012
Dahlquist, Germund; Eisenstat, Stanley C.; Golub, Gene H.
20
1972
Extrapolation of asymptotic expansions by a modified Aitken \(delta^ 2- \)formula. Zbl 0461.65003
Bjorstad, Petter; Dahlquist, Germund; Grosse, Eric
19
1981
Some properties of linear multistep and one-leg methods for ordinary differential equations. Zbl 0489.65044
Dahlquist, Germund
14
1979
Positive functions and some applications to stability questions for numerical methods. Zbl 0457.65049
Dahlquist, Germund
14
1978
Are the numerical methods and software satisfactory for chemical kinetics? Zbl 0535.65052
Dahlquist, Germund; Edsberg, Lennart; Sköllermo, Gunilla; Söderlind, Gustaf
13
1982
Bounds for the error in linear systems. Zbl 0417.65018
Dahlquist, Germund; Golub, Gene H.; Nash, Stephen G.
12
1979
Convergence acceleration from the point of view of linear programming. Zbl 0146.14202
Dahlquist, G.; Gustafson, Sven-Åke; Siklosi, K.
11
1965
A numerical method for some ordinary differential equations with large Lipschitz constants. Zbl 0194.18803
Dahlquist, G.
10
1969
On summation formulas due to Plana, Lindelöf and Abel, and related Gauss-Christoffel rules. I. Zbl 0878.65002
Dahlquist, Germund
10
1997
On the uniform power-boundedness of a family of matrices and the applications to one-leg and linear multistep methods. Zbl 0526.65051
Dahlquist, Germund; Huang, Mingyou; LeVeque, Randall
10
1983
On the analytic continuation of Eulerian products. Zbl 0046.27205
Dahlquist, Germund
9
1952
On the relation of G-stability to other stability concepts for linear multistep methods. Zbl 0438.65073
Dahlquist, Germund
8
1977
Gram polynomials and the Kummer function. Zbl 0931.33005
Barnard, R. W.; Dahlquist, G.; Pearce, K.; Reichel, L.; Richards, K. C.
7
1998
Shifted Runge-Kutta methods and transplanted differential equations. Zbl 0687.65077
Dahlquist, G.; Jeltsch, R.
7
1988
Some contractivity questions for one-leg- and linear multistep methods. Zbl 0489.65045
Dahlquist, Germund
7
1979
On the local and global errors of one-leg methods. Zbl 0475.65044
Dahlquist, Germund
7
1981
Convergence and stability for a hyperbolic difference equation with analytic initial-values. Zbl 0055.35801
Dahlquist, Germund
6
1954
33 years of numerical instability. I. Zbl 0579.65090
Dahlquist, Germund
6
1985
Some problems related to stiff nonlinear differential systems. Zbl 0499.65044
Dahlquist, Germund; Soederlind, Gustaf
6
1982
On the design of nested iterations for elliptic difference equations. Zbl 0244.65073
Kronsjö, Lydia; Dahlquist, Germund
6
1972
Some properties of linear multistep and one-leg methods for ordinary differential equations. Zbl 0436.65048
Dahlquist, Germund
6
1979
On summation formulas due to Plana, Lindelöf and Abel, and related Gauss-Christoffel rules. III. Zbl 0926.65001
Dahlquist, Germund
5
1999
Comparison of the method of averages with the method fo least squares. Zbl 0176.46303
Dahlquist, G.; Sjöberg, B.; Svensson, P.
5
1968
Fehlerabschätzungen bei Differenzenmethoden zur numerischen Integration gewöhnlicher Differentialgleichungen. Zbl 0043.33601
Dahlquist, Germund
5
1951
On matrix majorants and minorants, with applications to differential equations. Zbl 0521.65028
Dahlquist, Germund
5
1983
On the computation of slowly convergent Fourier integrals. Zbl 0253.65075
Gustafson, Sven-Åke; Dahlquist, G.
5
1972
On summation formulas due to Plana, Lindelöf and Abel, and related Gauss-Christoffel rules. II. Zbl 0893.65001
Dahlquist, Germund
5
1997
A “multigrid” extension of the \(FFT\) for the numerical inversion of Fourier and Laplace transforms. Zbl 0776.65069
Dahlquist, Germund
4
1993
On transformations of graded matrices, with applications to stiff ODE’s. Zbl 0599.65020
Dahlquist, Germund
4
1985
Stability questions for some numerical methods for ordinary differential equations. Zbl 0123.32405
Dahlquist, Germund G.
4
1963
Error propagation in stiff differential systems of singular perturbation type. Zbl 0473.65043
Soederlind, Gustaf; Dahlquist, Germund
4
1981
On rigorous error bounds in the numerical solution of ordinary differential equations. Zbl 0161.12403
Dahlquist, G. G.
3
1966
On the control of the global error in stiff initial value problems. Zbl 0473.65046
Dahlquist, Germund
3
1982
Die Monte-Carlo-Methode. Zbl 0056.12201
Dahlquist, Germund
2
1954
On an inverse non-linear diffusion problem. Zbl 0518.65065
Eriksson, Gerd; Dahlquist, Germund
2
1983
Numerische Methoden. Aus dem Schwedischen übers. von Norbert Krier und Peter Spellucci. 2., unveraend. Aufl. Zbl 0483.65002
Bjoerck, Ake; Dahlquist, Germund
2
1979
A multigrid FFT algorithm for slowly convergent inverse Laplace transforms. Zbl 0822.65122
Dahlquist, Germund
1
1994
Numerical methods in scientific computing. Vol. 1. Zbl 1153.65001
Dahlquist, Germund; Björck, Åke
152
2008
Reducibility and contractivity of Runge-Kutta methods revisited. Zbl 1106.65062
Dahlquist, Germund; Jeltsch, Rolf
39
2006
Numerical methods. Translated from the Swedish by Ned Anderson. Reprint of the 1974 English translation. Zbl 1029.65002
Dahlquist, Germund; Björck, Åke
32
2003
On summation formulas due to Plana, Lindelöf and Abel, and related Gauss-Christoffel rules. III. Zbl 0926.65001
Dahlquist, Germund
5
1999
Gram polynomials and the Kummer function. Zbl 0931.33005
Barnard, R. W.; Dahlquist, G.; Pearce, K.; Reichel, L.; Richards, K. C.
7
1998
On summation formulas due to Plana, Lindelöf and Abel, and related Gauss-Christoffel rules. I. Zbl 0878.65002
Dahlquist, Germund
10
1997
On summation formulas due to Plana, Lindelöf and Abel, and related Gauss-Christoffel rules. II. Zbl 0893.65001
Dahlquist, Germund
5
1997
A multigrid FFT algorithm for slowly convergent inverse Laplace transforms. Zbl 0822.65122
Dahlquist, Germund
1
1994
A “multigrid” extension of the \(FFT\) for the numerical inversion of Fourier and Laplace transforms. Zbl 0776.65069
Dahlquist, Germund
4
1993
Shifted Runge-Kutta methods and transplanted differential equations. Zbl 0687.65077
Dahlquist, G.; Jeltsch, R.
7
1988
33 years of numerical instability. I. Zbl 0579.65090
Dahlquist, Germund
6
1985
On transformations of graded matrices, with applications to stiff ODE’s. Zbl 0599.65020
Dahlquist, Germund
4
1985
Stability of two-step methods for variable integration steps. Zbl 0526.65049
Dahlquist, Germund G.; Liniger, Werner; Nevanlinna, Olavi
32
1983
On one-leg multistep methods. Zbl 0529.65048
Dahlquist, Germund
23
1983
On the uniform power-boundedness of a family of matrices and the applications to one-leg and linear multistep methods. Zbl 0526.65051
Dahlquist, Germund; Huang, Mingyou; LeVeque, Randall
10
1983
On matrix majorants and minorants, with applications to differential equations. Zbl 0521.65028
Dahlquist, Germund
5
1983
On an inverse non-linear diffusion problem. Zbl 0518.65065
Eriksson, Gerd; Dahlquist, Germund
2
1983
Are the numerical methods and software satisfactory for chemical kinetics? Zbl 0535.65052
Dahlquist, Germund; Edsberg, Lennart; Sköllermo, Gunilla; Söderlind, Gustaf
13
1982
Some problems related to stiff nonlinear differential systems. Zbl 0499.65044
Dahlquist, Germund; Soederlind, Gustaf
6
1982
On the control of the global error in stiff initial value problems. Zbl 0473.65046
Dahlquist, Germund
3
1982
Extrapolation of asymptotic expansions by a modified Aitken \(delta^ 2- \)formula. Zbl 0461.65003
Bjorstad, Petter; Dahlquist, Germund; Grosse, Eric
19
1981
On the local and global errors of one-leg methods. Zbl 0475.65044
Dahlquist, Germund
7
1981
Error propagation in stiff differential systems of singular perturbation type. Zbl 0473.65043
Soederlind, Gustaf; Dahlquist, Germund
4
1981
Some properties of linear multistep and one-leg methods for ordinary differential equations. Zbl 0489.65044
Dahlquist, Germund
14
1979
Bounds for the error in linear systems. Zbl 0417.65018
Dahlquist, Germund; Golub, Gene H.; Nash, Stephen G.
12
1979
Some contractivity questions for one-leg- and linear multistep methods. Zbl 0489.65045
Dahlquist, Germund
7
1979
Some properties of linear multistep and one-leg methods for ordinary differential equations. Zbl 0436.65048
Dahlquist, Germund
6
1979
Numerische Methoden. Aus dem Schwedischen übers. von Norbert Krier und Peter Spellucci. 2., unveraend. Aufl. Zbl 0483.65002
Bjoerck, Ake; Dahlquist, Germund
2
1979
G-stability is equivalent to A-stability. Zbl 0413.65057
Dahlquist, Germund
114
1978
On accuracy and unconditional stability of linear multistep methods for second order differential equations. Zbl 0378.65043
Dahlquist, Germund
75
1978
Positive functions and some applications to stability questions for numerical methods. Zbl 0457.65049
Dahlquist, Germund
14
1978
On the relation of G-stability to other stability concepts for linear multistep methods. Zbl 0438.65073
Dahlquist, Germund
8
1977
Error analysis for a class of methods for stiff non-linear initial value problems. Zbl 0352.65042
Dahlquist, Germund
86
1976
Problems related to the numerical treatment of stiff differential equations. Zbl 0275.65023
Dahlquist, Germund
28
1974
Bounds for the error of linear systems of equations using the theory of moments. Zbl 0238.65012
Dahlquist, Germund; Eisenstat, Stanley C.; Golub, Gene H.
20
1972
On the design of nested iterations for elliptic difference equations. Zbl 0244.65073
Kronsjö, Lydia; Dahlquist, Germund
6
1972
On the computation of slowly convergent Fourier integrals. Zbl 0253.65075
Gustafson, Sven-Åke; Dahlquist, G.
5
1972
A numerical method for some ordinary differential equations with large Lipschitz constants. Zbl 0194.18803
Dahlquist, G.
10
1969
Comparison of the method of averages with the method fo least squares. Zbl 0176.46303
Dahlquist, G.; Sjöberg, B.; Svensson, P.
5
1968
On rigorous error bounds in the numerical solution of ordinary differential equations. Zbl 0161.12403
Dahlquist, G. G.
3
1966
Convergence acceleration from the point of view of linear programming. Zbl 0146.14202
Dahlquist, G.; Gustafson, Sven-Åke; Siklosi, K.
11
1965
A special stability problem for linear multistep methods. Zbl 0123.11703
Dahlquist, Germund G.
454
1963
Stability questions for some numerical methods for ordinary differential equations. Zbl 0123.32405
Dahlquist, Germund G.
4
1963
Stability and error bounds in the numerical integration of ordinary differential equations. Zbl 0085.33401
Dahlquist, Germund
148
1959
Convergence and stability in the numerical integration of ordinary differential equations. Zbl 0071.11803
Dahlquist, Germund
168
1956
Convergence and stability for a hyperbolic difference equation with analytic initial-values. Zbl 0055.35801
Dahlquist, Germund
6
1954
Die Monte-Carlo-Methode. Zbl 0056.12201
Dahlquist, Germund
2
1954
On the analytic continuation of Eulerian products. Zbl 0046.27205
Dahlquist, Germund
9
1952
Fehlerabschätzungen bei Differenzenmethoden zur numerischen Integration gewöhnlicher Differentialgleichungen. Zbl 0043.33601
Dahlquist, Germund
5
1951
all top 5

Cited by 1,540 Authors

20 Hojjati, Gholamreza
19 Abdi, Ali
18 Nevanlinna, Olavi
17 Butcher, John C.
16 Spijker, Marc N.
16 Zlatev, Zahari
14 Zhang, Chengjian
13 Hairer, Ernst
13 Jeltsch, Rolf
12 Dahlquist, Germund
12 Lubich, Christian
11 Wang, Wansheng
10 Brugnano, Luigi
10 Cash, Jeff R.
10 Ikhile, Monday Ndidi Oziegbe
10 Tamma, Kumar K.
9 Hundsdorfer, Willem H.
9 Layton, William J.
9 Li, Shoufu
9 Nørsett, Syvert Paul
9 Ramos, Higinio
9 Söderlind, Gustaf
9 Trenchea, Catalin
8 Fatunla, Simeon Ola
8 Fung, Tsz Chai
8 Kohaupt, Ludwig G.
8 Kraaijevanger, J. F. B. M.
8 Sanz-Serna, Jesús María
8 Strehmel, Karl
8 Wen, Liping
7 Akrivis, Georgios D.
7 Ansorge, Rainer
7 Havasi, Ágnes
7 Huang, Chengming
7 Liniger, Werner
7 Milovanović, Gradimir V.
7 Moradi, Afsaneh
7 Verwer, Jan G.
7 Weiner, Rüdiger
7 Xiao, Aiguo
6 Auzinger, Winfried
6 Faragó, István
6 Frank, Reinhard
6 Gustafson, Sven-Åke
6 Iavernaro, Felice
6 Kovacs, Balazs A.
6 Li, Jiyong
6 Mohanty, Ranjan Kumar
6 Ogunfeyitimi, S. E.
6 Trigiante, Donato
6 Wanner, Gerhard
5 Axelsson, Axel Owe Holger
5 Chang, Shuenn-Yih
5 Cooper, Gavin J.
5 Dimov, Ivan Todor
5 Georgiev, Krassimir
5 Golub, Gene Howard
5 Hill, Adrian T.
5 Homeier, Herbert H. H.
5 Iserles, Arieh
5 Ketcheson, David I.
5 Kirlinger, Gabriela
5 Kulikov, Gennady Yur’evich
5 Maxam, Dean J.
5 Okunuga, Solomon A.
5 Reichel, Lothar
5 Senu, Norazak
5 Shampine, Lawrence Fred
5 Weniger, Ernst Joachim
5 Woźny, Paweł
5 Xu, Da
5 Zhou, Xiangmin
4 Abdulganiy, Ridwanulahi Iyanda
4 Akinfenwa, Olusheye Aremu Akin
4 Area, Iván
4 Baccouch, Mahboub
4 Brunner, Hermann
4 Burrage, Kevin
4 Chawla, Man M.
4 DeCaria, Victor P.
4 Engquist, Bjorn E.
4 Hillion, Pierre T. M.
4 Ibrahim, Zarina Bibi Binti
4 Ismail, Fudziah Bt.
4 Jator, Samuel N.
4 Kanwar, Vinay
4 Keller, Paweł
4 Lambers, James V.
4 Masjed-Jamei, Mohammad
4 McKee, Sean
4 Meurant, Gérard A.
4 Okuonghae, Robert I.
4 Oliveira, Paula
4 Owren, Brynjulf
4 Pei, Wenlong
4 Qin, Yi
4 Qureshi, Sania
4 Reimer, Manfred
4 Rokhlin, Vladimir
4 Schneid, Josef
...and 1,440 more Authors
all top 5

Cited in 240 Serials

94 BIT
91 Journal of Computational and Applied Mathematics
81 Numerische Mathematik
64 Applied Numerical Mathematics
59 Mathematics of Computation
56 Applied Mathematics and Computation
51 BIT. Nordisk Tidskrift for Informationsbehandling
38 Journal of Computational Physics
38 Numerical Algorithms
35 Computers & Mathematics with Applications
32 Computer Methods in Applied Mechanics and Engineering
28 International Journal of Computer Mathematics
26 Computing
20 International Journal for Numerical Methods in Engineering
19 Journal of Scientific Computing
18 SIAM Journal on Numerical Analysis
17 Mathematics and Computers in Simulation
16 Journal of Mathematical Analysis and Applications
16 SIAM Journal on Scientific Computing
11 Computer Physics Communications
11 Applied Mathematics Letters
11 Advances in Computational Mathematics
10 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
10 Applied Mathematical Modelling
9 Journal of Mathematical Chemistry
9 Communications in Nonlinear Science and Numerical Simulation
8 Numerical Methods for Partial Differential Equations
8 Computational and Applied Mathematics
8 International Journal of Applied and Computational Mathematics
7 Mathematical Methods in the Applied Sciences
7 Aplikace Matematiky
7 Journal of the Nigerian Mathematical Society
6 Calcolo
6 SIAM Journal on Matrix Analysis and Applications
6 Mathematical Problems in Engineering
5 International Journal of Mathematical Education in Science and Technology
5 Automatica
5 Mathematische Zeitschrift
5 Linear Algebra and its Applications
5 Journal of the Korean Society for Industrial and Applied Mathematics
4 Computers and Fluids
4 International Journal of Control
4 Numerical Functional Analysis and Optimization
4 Computational Mechanics
4 Computational Mathematics and Mathematical Physics
4 Applied and Computational Harmonic Analysis
4 Numerical Linear Algebra with Applications
4 Advances in Difference Equations
4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
4 Afrika Matematika
3 ZAMP. Zeitschrift für angewandte Mathematik und Physik
3 Stochastic Analysis and Applications
3 Journal of Complexity
3 COMPEL
3 Celestial Mechanics
3 Communications in Statistics. Theory and Methods
3 International Journal of Computational Fluid Dynamics
3 Abstract and Applied Analysis
3 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
3 Discrete Dynamics in Nature and Society
3 Mathematical Modelling and Analysis
3 Foundations of Computational Mathematics
3 Journal of Applied Mathematics
3 Journal of Applied Mathematics and Computing
3 International Journal of Computational Methods
2 Applicable Analysis
2 Communications on Pure and Applied Mathematics
2 Journal of the Franklin Institute
2 Journal of Mathematical Physics
2 Mathematical Biosciences
2 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
2 Functiones et Approximatio. Commentarii Mathematici
2 Journal of Number Theory
2 Meccanica
2 Publications of the Research Institute for Mathematical Sciences, Kyoto University
2 Mathematical and Computer Modelling
2 Multidimensional Systems and Signal Processing
2 Japan Journal of Industrial and Applied Mathematics
2 Communications in Statistics. Simulation and Computation
2 SIAM Journal on Mathematical Analysis
2 Celestial Mechanics and Dynamical Astronomy
2 Journal of Nonlinear Science
2 International Journal of Numerical Methods for Heat & Fluid Flow
2 Parallel Algorithms and Applications
2 Journal of Vibration and Control
2 Lobachevskii Journal of Mathematics
2 International Journal of Nonlinear Sciences and Numerical Simulation
2 The ANZIAM Journal
2 Differential Equations
2 Archives of Computational Methods in Engineering
2 Discrete and Continuous Dynamical Systems. Series B
2 Computational Methods in Applied Mathematics
2 Journal of Numerical Mathematics
2 SIAM Journal on Applied Dynamical Systems
2 Multiscale Modeling & Simulation
2 International Journal of Numerical Analysis and Modeling
2 Nonlinear Analysis. Hybrid Systems
2 International Journal of Structural Stability and Dynamics
2 Statistics and Computing
2 Nonlinear Analysis. Theory, Methods & Applications
...and 140 more Serials
all top 5

Cited in 48 Fields

1,068 Numerical analysis (65-XX)
354 Ordinary differential equations (34-XX)
163 Partial differential equations (35-XX)
70 Fluid mechanics (76-XX)
55 Mechanics of deformable solids (74-XX)
48 Approximations and expansions (41-XX)
46 Mechanics of particles and systems (70-XX)
39 Dynamical systems and ergodic theory (37-XX)
39 Integral equations (45-XX)
32 Probability theory and stochastic processes (60-XX)
32 Systems theory; control (93-XX)
31 Linear and multilinear algebra; matrix theory (15-XX)
28 Computer science (68-XX)
22 Statistics (62-XX)
16 Special functions (33-XX)
16 Operator theory (47-XX)
16 Quantum theory (81-XX)
15 Biology and other natural sciences (92-XX)
14 Operations research, mathematical programming (90-XX)
11 Number theory (11-XX)
11 Difference and functional equations (39-XX)
10 History and biography (01-XX)
10 Real functions (26-XX)
10 Optics, electromagnetic theory (78-XX)
9 Integral transforms, operational calculus (44-XX)
9 Calculus of variations and optimal control; optimization (49-XX)
8 Functions of a complex variable (30-XX)
8 Sequences, series, summability (40-XX)
8 Harmonic analysis on Euclidean spaces (42-XX)
8 Statistical mechanics, structure of matter (82-XX)
8 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
8 Information and communication theory, circuits (94-XX)
7 Classical thermodynamics, heat transfer (80-XX)
7 Geophysics (86-XX)
4 Combinatorics (05-XX)
3 General and overarching topics; collections (00-XX)
2 Mathematical logic and foundations (03-XX)
2 Field theory and polynomials (12-XX)
2 Algebraic geometry (14-XX)
2 Measure and integration (28-XX)
2 Several complex variables and analytic spaces (32-XX)
2 Global analysis, analysis on manifolds (58-XX)
2 Relativity and gravitational theory (83-XX)
1 Potential theory (31-XX)
1 Functional analysis (46-XX)
1 Differential geometry (53-XX)
1 Astronomy and astrophysics (85-XX)
1 Mathematics education (97-XX)

Citations by Year

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