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Frank, Reinhard

Co-Author Distance
Author ID: frank.reinhard Recent zbMATH articles by "Frank, Reinhard"
Published as: Frank, R.; Frank, Reinhard
Documents Indexed: 31 Publications since 1975
Co-Authors: 8 Co-Authors with 28 Joint Publications
96 Co-Co-Authors
all top 5

Co-Authors

3 single-authored
13 Auzinger, Winfried
11 Überhuber, Christoph W.
6 Kirlinger, Gabriela
5 Hertling, Jörg
5 Macsek, Franz Karl
5 Schneid, Josef
1 Monnet, J. P.
1 Stetter, Hans J.
all top 5

Serials

6 Computing
4 Numerische Mathematik
4 SIAM Journal on Numerical Analysis
3 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
3 Applied Numerical Mathematics
1 Mathematics of Computation
1 BIT
1 Journal of Computational and Applied Mathematics
1 SIAM Journal on Scientific and Statistical Computing
1 BIT. Nordisk Tidskrift for Informationsbehandling
1 Beiträge zur Numerischen Mathematik

Fields

31 Numerical analysis (65-XX)
19 Ordinary differential equations (34-XX)
3 Partial differential equations (35-XX)
1 History and biography (01-XX)
1 Computer science (68-XX)

Publications by Year

all cited Publications top 5 cited Publications

Citations contained in zbMATH Open

27 Publications have been cited 459 times in 256 Documents Cited by ▼ Year ▼
The concept of B-convergence. Zbl 0467.65032
Frank, Reinhard; Schneid, Josef; Ueberhuber, Christoph W.
83
1981
Order results for implicit Runge-Kutta methods applied to stiff systems. Zbl 0577.65056
Frank, Reinhard; Schneid, Josef; Ueberhuber, Christoph W.
69
1985
Stability properties of implicit Runge-Kutta methods. Zbl 0577.65055
Frank, Reinhard; Schneid, Josef; Ueberhuber, Christoph W.
52
1985
Iterated defect correction for the efficient solution of stiff systems of ordinary differential equations. Zbl 0364.65053
Frank, Reinhard; Ueberhuber, Christoph W.
48
1977
Asymptotic error expansions for stiff equations: An analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case. Zbl 0684.65075
Auzinger, W.; Frank, R.
35
1989
Iterated defect correction for differential equations. I: Theoretical results. Zbl 0401.65046
Frank, R.; Ueberhuber, C. W.
22
1978
Asymptotic error expansions for stiff equations: The implicit Euler scheme. Zbl 0688.65056
Auzinger, W.; Frank, R.; Macsek, F.
21
1990
The method of iterated defect-correction and its application to two-point boundary value problems. I. Zbl 0346.65034
Frank, Reinhard
20
1976
A note on convergence concepts for stiff problems. Zbl 0719.65058
Auzinger, W.; Frank, R.; Kirlinger, G.
12
1990
The method of iterated defect-correction and its application to two-point boundary value problems. II. Zbl 0366.65034
Frank, R.
12
1977
The application of iterated defect correction to variational methods for elliptic boundary value problems. Zbl 0498.65051
Frank, R.; Hertling, J.; Monnet, J. P.
11
1983
Schätzungen des globalen Diskretisierungsfehlers bei Runge-Kutta- Methoden. Zbl 0319.65049
Frank, Reinhard
7
1975
Modern convergence theory for stiff initial-value problems. Zbl 0782.65087
Auzinger, W.; Frank, R.; Kirlinger, G.
7
1993
Extending convergence theory for nonlinear stiff problems. I. Zbl 0863.65040
Auzinger, W.; Frank, R.; Kirlinger, G.
7
1996
Asymptotic error expansions for stiff equations: Applications. Zbl 0688.65057
Auzinger, W.; Frank, R.; Kirlinger, G.
6
1990
B-convergence properties of defect correction methods. I, II. Zbl 0619.65061
Frank, R.; Hertling, J.; Lehner, H.
6
1986
B-convergence: A survey. Zbl 0674.65056
Frank, Reinhard; Schneid, Josef; Ueberhuber, Christoph W.
5
1989
An extension of B-convergence for Runge-Kutta methods. Zbl 0747.65056
Auzinger, W.; Frank, R.; Kirlinger, G.
5
1992
An extension of the applicability of iterated deferred corrections. Zbl 0379.65003
Frank, Reinhard; Hertling, Joerg; Ueberhuber, Christoph W.
5
1977
Collocation and iterated defect correction. Zbl 0392.65032
Frank, Reinhard; Ueberhuber, Christoph W.
5
1978
On asymptotic expansions of the discretization error for stiff equations. Zbl 0689.65046
Auzinger, Winfried; Frank, Reinhard; Macsek, Franz
4
1988
Die Anwendung der iterierten Defektkorrektur auf das Dirichletproblem. Zbl 0421.65061
Frank, Reinhard; Hertling, Jörg
4
1979
Asymptotic error expansions for defect correction iterates. Zbl 0526.65056
Frank, R.; Macsek, F.; Ueberhuber, C. W.
4
1984
Asymptotic expansions of the global discretization error for stiff problems. Zbl 0677.65077
Auzinger, W.; Frank, R.
3
1989
Vienna contributions to the development of RK-methods. Zbl 0870.65062
Auzinger, Winfried; Frank, Reinhard; Stetter, Hans J.
3
1996
Iterated defect correction of differential equations. II: Numerical experiments. Zbl 0546.65076
Frank, R.; Macsek, F.; Ueberhuber, C. W.
2
1984
Defect correction algorithms for stiff ordinary differential equations. Zbl 0553.65054
Frank, R.; Hertling, J.; Lehner, H.
1
1984
Extending convergence theory for nonlinear stiff problems. I. Zbl 0863.65040
Auzinger, W.; Frank, R.; Kirlinger, G.
7
1996
Vienna contributions to the development of RK-methods. Zbl 0870.65062
Auzinger, Winfried; Frank, Reinhard; Stetter, Hans J.
3
1996
Modern convergence theory for stiff initial-value problems. Zbl 0782.65087
Auzinger, W.; Frank, R.; Kirlinger, G.
7
1993
An extension of B-convergence for Runge-Kutta methods. Zbl 0747.65056
Auzinger, W.; Frank, R.; Kirlinger, G.
5
1992
Asymptotic error expansions for stiff equations: The implicit Euler scheme. Zbl 0688.65056
Auzinger, W.; Frank, R.; Macsek, F.
21
1990
A note on convergence concepts for stiff problems. Zbl 0719.65058
Auzinger, W.; Frank, R.; Kirlinger, G.
12
1990
Asymptotic error expansions for stiff equations: Applications. Zbl 0688.65057
Auzinger, W.; Frank, R.; Kirlinger, G.
6
1990
Asymptotic error expansions for stiff equations: An analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case. Zbl 0684.65075
Auzinger, W.; Frank, R.
35
1989
B-convergence: A survey. Zbl 0674.65056
Frank, Reinhard; Schneid, Josef; Ueberhuber, Christoph W.
5
1989
Asymptotic expansions of the global discretization error for stiff problems. Zbl 0677.65077
Auzinger, W.; Frank, R.
3
1989
On asymptotic expansions of the discretization error for stiff equations. Zbl 0689.65046
Auzinger, Winfried; Frank, Reinhard; Macsek, Franz
4
1988
B-convergence properties of defect correction methods. I, II. Zbl 0619.65061
Frank, R.; Hertling, J.; Lehner, H.
6
1986
Order results for implicit Runge-Kutta methods applied to stiff systems. Zbl 0577.65056
Frank, Reinhard; Schneid, Josef; Ueberhuber, Christoph W.
69
1985
Stability properties of implicit Runge-Kutta methods. Zbl 0577.65055
Frank, Reinhard; Schneid, Josef; Ueberhuber, Christoph W.
52
1985
Asymptotic error expansions for defect correction iterates. Zbl 0526.65056
Frank, R.; Macsek, F.; Ueberhuber, C. W.
4
1984
Iterated defect correction of differential equations. II: Numerical experiments. Zbl 0546.65076
Frank, R.; Macsek, F.; Ueberhuber, C. W.
2
1984
Defect correction algorithms for stiff ordinary differential equations. Zbl 0553.65054
Frank, R.; Hertling, J.; Lehner, H.
1
1984
The application of iterated defect correction to variational methods for elliptic boundary value problems. Zbl 0498.65051
Frank, R.; Hertling, J.; Monnet, J. P.
11
1983
The concept of B-convergence. Zbl 0467.65032
Frank, Reinhard; Schneid, Josef; Ueberhuber, Christoph W.
83
1981
Die Anwendung der iterierten Defektkorrektur auf das Dirichletproblem. Zbl 0421.65061
Frank, Reinhard; Hertling, Jörg
4
1979
Iterated defect correction for differential equations. I: Theoretical results. Zbl 0401.65046
Frank, R.; Ueberhuber, C. W.
22
1978
Collocation and iterated defect correction. Zbl 0392.65032
Frank, Reinhard; Ueberhuber, Christoph W.
5
1978
Iterated defect correction for the efficient solution of stiff systems of ordinary differential equations. Zbl 0364.65053
Frank, Reinhard; Ueberhuber, Christoph W.
48
1977
The method of iterated defect-correction and its application to two-point boundary value problems. II. Zbl 0366.65034
Frank, R.
12
1977
An extension of the applicability of iterated deferred corrections. Zbl 0379.65003
Frank, Reinhard; Hertling, Joerg; Ueberhuber, Christoph W.
5
1977
The method of iterated defect-correction and its application to two-point boundary value problems. I. Zbl 0346.65034
Frank, Reinhard
20
1976
Schätzungen des globalen Diskretisierungsfehlers bei Runge-Kutta- Methoden. Zbl 0319.65049
Frank, Reinhard
7
1975
all cited Publications top 5 cited Publications
all top 5

Cited by 293 Authors

16 Frank, Reinhard
14 Auzinger, Winfried
10 Schneid, Josef
9 Li, Shoufu
8 Kirlinger, Gabriela
8 Si, Zhiyong
7 Butcher, John C.
7 Hundsdorfer, Willem H.
7 Kraaijevanger, J. F. B. M.
7 Spijker, Marc N.
6 Burrage, Kevin
6 Cooper, Gavin J.
6 Dekker, Kees
6 Hairer, Ernst
6 Überhuber, Christoph W.
6 Verwer, Jan G.
6 Weinmüller, Ewa B.
6 Xiao, Aiguo
5 Chan, Robert Peng Kong
4 Chen, Guangnan
4 Fu, Hongyuan
4 He, Yinnian
4 Koch, Othmar
4 Lubich, Christian
4 Sanz-Serna, Jesús María
4 Shahzad, Naseer
4 Somali, Sennur
4 Weiner, Rüdiger
3 Aggul, Mustafa
3 Alghamdi, Maryam A.
3 Cash, Jeff R.
3 Erkmen, Dilek
3 Huang, Chengming
3 Jackiewicz, Zdzislaw
3 Labovsky, Alexander E.
3 Minion, Michael L.
3 Ostermann, Alexander
3 Schmitt, Bernhard A.
3 Strehmel, Karl
3 Vignesvaran, R.
3 Wang, Yunxia
3 Xu, Hong-Kun
3 Xu, Yang
3 Yuan, Haiyan
3 Zhao, Jingjun
2 Aibinu, Mathew Olajiire
2 Amat Plata, Sergio
2 Axelsson, Axel Owe Holger
2 Baier, Robert
2 Böhmer, Klaus
2 Choo, Joshua Y.
2 Christlieb, Andrew J.
2 Çibik, Aytekin Bayram
2 Dumbser, Michael
2 El-Hawary, H. M.
2 Farkhi, Elza M.
2 Filimon, Alexander
2 Gan, Siqing
2 González-Pinto, Severiano
2 Hansen, Eskil
2 Hertling, Jörg
2 Hofstätter, Harald
2 Huang, Jingfang
2 Ismail, Fudziah Bt.
2 Kaya, Songul
2 Kumam, Poom
2 Kvaerno, Anne
2 Legaz, María José
2 Liu, Jun
2 Liu, Mingzhu
2 Macsek, Franz Karl
2 Mahmoud, Suliman M.
2 Mewomo, Oluwatosin Temitope
2 Monnet, J. P.
2 Montijano, Juan Ignacio
2 Munz, Claus-Dieter
2 Musa, Harald
2 Owren, Brynjulf
2 Pakkaranang, Nuttapol
2 Pedregal, Pablo
2 Sathiaraj, D. Daniel
2 Senu, Norazak
2 Stetter, Hans J.
2 Suleiman, Mohamed Bin
2 Sunthrayuth, Pongsakorn
2 van Niekerk, Frederik D.
2 Wang, Kun
2 Wang, Wansheng
2 Wang, Yan
2 Wanner, Gerhard
2 Wen, Liping
2 Zhan, Rui
2 Zhang, Jianguo
2 Zuo, Yijun
1 Adams, Nikolaus A.
1 Ahmad, Bashir
1 Ahmed, Maqbool
1 Aïd, René
1 Alamri, Yousef
1 Alexander, Roger K.
...and 193 more Authors
all top 5

Cited in 67 Serials

28 BIT
27 Applied Numerical Mathematics
25 Numerische Mathematik
21 Computing
21 Journal of Computational and Applied Mathematics
11 International Journal of Computer Mathematics
9 Computers & Mathematics with Applications
9 Journal of Computational Physics
9 Applied Mathematics and Computation
7 Mathematics of Computation
7 Numerical Algorithms
6 Journal of Nonlinear Science and Applications
4 Journal of Scientific Computing
3 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
3 Journal of Applied Mathematics
3 Fixed Point Theory and Applications
3 BIT. Nordisk Tidskrift for Informationsbehandling
2 Applicable Analysis
2 Mathematics and Computers in Simulation
2 SIAM Journal on Numerical Analysis
2 Numerical Methods for Partial Differential Equations
2 SIAM Journal on Scientific Computing
2 Mathematical Problems in Engineering
2 Abstract and Applied Analysis
2 Journal of Inequalities and Applications
1 Computers and Fluids
1 Computer Methods in Applied Mechanics and Engineering
1 Journal of Mathematical Analysis and Applications
1 Mathematical Methods in the Applied Sciences
1 Aplikace Matematiky
1 Calcolo
1 International Journal of Mathematics and Mathematical Sciences
1 Journal of Differential Equations
1 Mathematische Zeitschrift
1 Numerical Functional Analysis and Optimization
1 Journal of Computational Mathematics
1 Acta Mathematicae Applicatae Sinica. English Series
1 Optimization
1 Applied Mathematics Letters
1 Mathematical and Computer Modelling
1 Journal of Integral Equations and Applications
1 Linear Algebra and its Applications
1 Computational Optimization and Applications
1 Numerical Linear Algebra with Applications
1 Computational and Applied Mathematics
1 Filomat
1 Taiwanese Journal of Mathematics
1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
1 Communications de la Faculté des Sciences de l’Université d’Ankara. Séries A1. Mathematics and Statistics
1 Computational Methods in Applied Mathematics
1 Journal of Numerical Mathematics
1 Journal of Applied Mathematics and Computing
1 Advances in Difference Equations
1 Boundary Value Problems
1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
1 The Journal of Prime Research in Mathematics
1 Frontiers of Mathematics in China
1 Communications in Computational Physics
1 Armenian Journal of Mathematics
1 Advances in Applied Mathematics and Mechanics
1 Science China. Mathematics
1 Journal of Mathematics and Computer Science. JMCS
1 Afrika Matematika
1 ISRN Applied Mathematics
1 Journal of Mathematics
1 Mathematics
1 Khayyam Journal of Mathematics
all top 5

Cited in 24 Fields

231 Numerical analysis (65-XX)
138 Ordinary differential equations (34-XX)
30 Partial differential equations (35-XX)
24 Operator theory (47-XX)
24 Fluid mechanics (76-XX)
7 Integral equations (45-XX)
6 History and biography (01-XX)
5 General topology (54-XX)
4 Geophysics (86-XX)
3 Dynamical systems and ergodic theory (37-XX)
3 Probability theory and stochastic processes (60-XX)
2 Linear and multilinear algebra; matrix theory (15-XX)
2 Approximations and expansions (41-XX)
2 Calculus of variations and optimal control; optimization (49-XX)
2 Mechanics of deformable solids (74-XX)
2 Classical thermodynamics, heat transfer (80-XX)
2 Quantum theory (81-XX)
2 Operations research, mathematical programming (90-XX)
1 Real functions (26-XX)
1 Difference and functional equations (39-XX)
1 Harmonic analysis on Euclidean spaces (42-XX)
1 Computer science (68-XX)
1 Statistical mechanics, structure of matter (82-XX)
1 Biology and other natural sciences (92-XX)

Citations by Year