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## Kloeden, Peter Eris

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 Author ID: kloeden.peter-eris Published as: Kloeden, Peter E.; Kloeden, P. E.; Kloeden, Peter; Kloeden, P.; Kloeden, Peter Eris; Kloeden, Peter. E.; Cloeden, P. Homepage: http://www.math.uni-frankfurt.de/~kloeden/ External Links: MGP
 Documents Indexed: 386 Publications since 1974, including 20 Books Biographic References: 2 Publications
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#### Co-Authors

 42 single-authored 46 Diamond, Phil 34 Pokrovskiĭ, Alexeĭ Vadimovich 30 Caraballo Garrido, Tomás 22 Kozyakin, Viktor Sergeevich 21 Han, Xiaoying 17 Yang, Meihua 15 Jentzen, Arnulf 14 Lorenz, Thomas 13 Platen, Eckhard 12 Schmalfuß, Björn 11 Real Anguas, José 10 Marín-Rubio, Pedro 10 Neuenkirch, Andreas 8 Wang, Yejuan 7 Asai, Yusuke 7 Cui, Hongyong 7 Grüne, Lars 7 Li, Desheng 7 Valero, José 7 Wu, Fuke 6 Pötzsche, Christian 6 Simsen, Jacson 5 Anh, Vo V. 5 Bennett, Andrew F. 5 Duan, Jinqiao 5 Pavani, Raffaella 5 Rasmussen, Martin 5 Vladimirov, Aleksandr Aleksandrovich 4 Cheban, David Nikolai 4 Higham, Desmond J. 4 Hilger, Stefan 4 Johnson, Russell Allan 4 Kleptsyna, Marina L. 4 Krasnosel’skiĭ, Aleksandr Markovich 4 Krasnosel’skiĭ, Mark Aleksandrovich 4 Rubinov, Alexander M. 4 Schropp, Johannes 4 Schurz, Henri 4 Siegmund, Stefan 3 Al-Nayef, Anwar A. 3 Chueshov, Igor’ Dmitrievich 3 Colonius, Fritz 3 Crauel, Hans 3 Halidias, Nikolaos 3 Hutzenthaler, Martin 3 Langa, Jose’ Antonio 3 Lorenz, Jens 3 Mao, Xuerong 3 Ombach, Jerzy 3 Pinelas, Sandra 3 Shardlow, Tony 3 Yang, Hao 2 Amigó, José María 2 Anguiano, María 2 Arnold, Ludwig 2 Balibrea, Francisco 2 Becker, Sebastian 2 Cyganowski, Sasha 2 Doan, Thai Son 2 Fabbri, Roberta 2 Garay, Barnabas M. 2 Gil’, Michael Iosif 2 Giménez, Angel 2 Graef, John R. 2 Huong, Phan Thi 2 Li, Zhong 2 Liu, Jicheng 2 Liu, Linfang 2 Liu, Xianming 2 Mustard, J. F. 2 Peng, Ling 2 Schoenmakers, John G. M. 2 Sonner, Stefanie 2 Sui, Meiyu 2 Sun, Chunyou 2 Sun, Wenlong 2 Vladimirov, Igor G. 2 Yang, Lu 2 Zhong, Chengkui 1 Albeverio, Sergio A. 1 Bobylev, Nikolaĭ Antonovich 1 Bondarenko, V. A. 1 Buckwar, Evelyn 1 Cao, Yanzhao 1 Ciepliński, Krzysztof 1 Collings, I. L. 1 Dajmond, F. 1 Došlá, Zuzana 1 Došlý, Ondřej 1 Dr. Son, Doan Thai 1 Dutton, John A. 1 Dzalilov, Zari A. 1 Fisher, Michael E. 1 Flandoli, Franco 1 Gao, Fengshuang 1 Garrido-Atienza, María José 1 Gerstner, Thomas 1 Gess, Benjamin 1 Giga, Yoshikazu 1 Grecksch, Wilfried ...and 58 more Co-Authors
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#### Serials

 17 Discrete and Continuous Dynamical Systems. Series B 16 Journal of Differential Equations 13 Bulletin of the Australian Mathematical Society 13 Journal of Difference Equations and Applications 12 Discrete and Continuous Dynamical Systems 12 Stochastics and Dynamics 11 Fuzzy Sets and Systems 10 Stochastic Analysis and Applications 10 Communications on Pure and Applied Analysis 8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Journal of the Australian Mathematical Society, Series B 7 Journal of Mathematical Analysis and Applications 7 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 6 Journal of Computational and Applied Mathematics 6 Journal of Applied Mathematics and Stochastic Analysis 6 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 5 BIT 5 Mathematische Nachrichten 5 Automation and Remote Control 5 Journal of Dynamics and Differential Equations 5 Set-Valued Analysis 5 Electronic Journal of Differential Equations (EJDE) 4 Numerische Mathematik 4 Nonlinear Analysis. Real World Applications 3 Applied Mathematics and Optimization 3 Numerical Functional Analysis and Optimization 3 SIAM Journal on Numerical Analysis 3 Physica D 3 The Annals of Applied Probability 3 Numerical Algorithms 3 Journal of the Australian Mathematical Society. Series A 3 SIAM Journal on Mathematical Analysis 3 Random & Computational Dynamics 3 Springer Proceedings in Mathematics & Statistics 3 Nonlinear Analysis. Theory, Methods & Applications 3 Electronic Research Archive 2 Computers & Mathematics with Applications 2 IMA Journal of Numerical Analysis 2 Journal of Statistical Physics 2 Mathematical Methods in the Applied Sciences 2 Problems of Information Transmission 2 Mathematika 2 Proceedings of the American Mathematical Society 2 Systems & Control Letters 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Journal of Nonlinear Science 2 Arab Journal of Mathematical Sciences 2 Revista Matemática Complutense 2 Advanced Nonlinear Studies 2 Interdisciplinary Mathematical Sciences 2 Discrete and Continuous Dynamical Systems. Series S 2 Set-Valued and Variational Analysis 2 Applications of Mathematics 2 Universitext 1 Geophysical and Astrophysical Fluid Dynamics 1 International Journal of Control 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Theoretical and Mathematical Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Bulletin of Mathematical Biology 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 The Annals of Probability 1 Annales Polonici Mathematici 1 Applied Mathematics and Computation 1 Glasgow Mathematical Journal 1 Journal of Applied Probability 1 Journal of Optimization Theory and Applications 1 Mathematics and Computers in Simulation 1 Results in Mathematics 1 Theoretical Computer Science 1 Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik 1 Mathematical and Computer Modelling 1 Asymptotic Analysis 1 Dynamics and Stability of Systems 1 Complex Systems 1 Stochastic Hydrology and Hydraulics 1 Annals of Operations Research 1 Applied Mathematical Modelling 1 European Journal of Operational Research 1 International Journal of Computer Mathematics 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 SIAM Journal on Applied Mathematics 1 SIAM Review 1 SIAM Journal on Scientific Computing 1 The Journal of Fuzzy Mathematics 1 Random Operators and Stochastic Equations 1 NoDEA. Nonlinear Differential Equations and Applications 1 Buletinul Academiei de Științe a Republicii Moldova. Matematica 1 Monte Carlo Methods and Applications 1 Dynamics of Continuous, Discrete and Impulsive Systems 1 Doklady Mathematics 1 Communications in Applied Analysis 1 Functional Differential Equations 1 Electronic Journal of Qualitative Theory of Differential Equations 1 Fractional Calculus & Applied Analysis 1 LMS Journal of Computation and Mathematics 1 Optimization and Engineering 1 Dynamical Systems 1 Journal of the Australian Mathematical Society ...and 25 more Serials
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#### Fields

 172 Dynamical systems and ergodic theory (37-XX) 128 Ordinary differential equations (34-XX) 112 Probability theory and stochastic processes (60-XX) 98 Numerical analysis (65-XX) 82 Partial differential equations (35-XX) 46 Systems theory; control (93-XX) 27 Difference and functional equations (39-XX) 25 Biology and other natural sciences (92-XX) 19 General topology (54-XX) 17 Fluid mechanics (76-XX) 16 Operator theory (47-XX) 12 General and overarching topics; collections (00-XX) 11 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Global analysis, analysis on manifolds (58-XX) 8 Mathematical logic and foundations (03-XX) 8 Real functions (26-XX) 7 Computer science (68-XX) 7 Geophysics (86-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 5 Integral equations (45-XX) 5 Operations research, mathematical programming (90-XX) 4 History and biography (01-XX) 4 Approximations and expansions (41-XX) 3 Functional analysis (46-XX) 3 Convex and discrete geometry (52-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Information and communication theory, circuits (94-XX) 1 Number theory (11-XX) 1 Measure and integration (28-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX)

#### Citations contained in zbMATH Open

310 Publications have been cited 6,275 times in 4,076 Documents Cited by Year
Numerical solution of stochastic differential equations. Zbl 0752.60043
Kloeden, Peter E.; Platen, Eckhard
1992
Higher-order implicit strong numerical schemes for stochastic differential equations. Zbl 0925.65261
Kloeden, P. E.; Platen, E.
1992
Metric spaces of fuzzy sets: theory and applications. Zbl 0873.54019
Diamond, Phil; Kloeden, Peter
1994
A survey of numerical methods for stochastic differential equations. Zbl 0701.60054
Kloeden, P. E.; Platen, E.
1989
Numerical methods for stochastic differential equations. Zbl 0858.65148
Kloeden, P. E.; Platen, E.
1995
Strong and weak divergence in finite time of Euler’s method for stochastic differential equations with non-globally Lipschitz continuous coefficients. Zbl 1228.65014
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
2011
Flattening, squeezing and the existence of random attractors. Zbl 1133.37323
Kloeden, Peter E.; Langa, José A.
2007
Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients. Zbl 1256.65003
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
2012
Numerical solution of SDE through computer experiments. Including floppy disk. Zbl 0789.65100
Kloeden, Peter E.; Platen, Eckhard; Schurz, Henri
1994
Multivalued spatial discretization of dynamical systems. Zbl 0843.54041
Diamond, P.; Pokrovskij, A.; Kloeden, P.
1994
Metric spaces of fuzzy sets. Zbl 0704.54006
Diamond, Phil; Kloeden, Peter
1990
Nonautonomous dynamical systems. Zbl 1244.37001
Kloeden, Peter E.; Rasmussen, Martin
2011
Numerical methods for nonlinear stochastic differential equations with jumps. Zbl 1186.65010
Higham, Desmond J.; Kloeden, Peter. E.
2005
Nonautonomous systems, cocycle attractors and variable time-step discretization. Zbl 0886.65077
Kloeden, Peter E.; Schmalfuß, Björn
1997
Exponentially stable stationary solutions for stochastic evolution equations and their perturbation. Zbl 1066.60058
Caraballo, Tomás; Kloeden, Peter E.; Schmalfuß, Björn
2004
The relationship between pullback, forward and global attractors of nonautonomous dynamical systems. Zbl 1054.34087
Cheban, D. N.; Kloeden, P. E.; Schmalfuß, B.
2002
Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space-time noise. Zbl 1186.65011
Jentzen, Arnulf; Kloeden, Peter E.
2009
Stable attracting sets in dynamical systems and in their one-step discretizations. Zbl 0613.65083
Kloeden, P. E.; Lorenz, J.
1986
Characterization of compact subsets of fuzzy sets. Zbl 0661.54011
Diamond, Phil; Kloeden, Peter
1989
Asymptotic behaviour of nonautonomous difference inclusions. Zbl 0902.93043
Kloeden, Peter E.; Schmalfuss, Björn
1998
Convergence and stability of implicit methods for jump-diffusion systems. Zbl 1109.65007
Higham, Desmond J.; Kloeden, Peter E.
2006
Recent developments in dynamical systems: three perspectives. Zbl 1202.37003
Balibrea, F.; Caraballo, T.; Kloeden, P. E.; Valero, J.
2010
Taylor approximations for stochastic partial differential equations. Zbl 1240.35001
Jentzen, Arnulf; Kloeden, Peter
2011
The numerical approximation of stochastic partial differential equations. Zbl 1205.60130
Jentzen, A.; Kloeden, P. E.
2009
Numerical solution of stochastic differential equations. 4th corrected printing. Zbl 1216.60052
Kloeden, Peter E.; Platen, Eckhard
2010
Time-discretised Galerkin approximations of parabolic stochastic PDEs. Zbl 0880.35143
Grecksch, W.; Kloeden, P. E.
1996
Strong convergence rates for backward Euler on a class of nonlinear jump-diffusion problems. Zbl 1128.65007
Higham, Desmond J.; Kloeden, Peter E.
2007
The pathwise convergence of approximation schemes for stochastic differential equations. Zbl 1223.60051
Kloeden, P. E.; Neuenkirch, A.
2007
Fuzzy dynamical systems. Zbl 0509.54040
Kloeden, P. E.
1982
Non-autonomous attractors for integro-differential evolution equations. Zbl 1185.45016
Caraballo, Tomás; Kloeden, P. E.
2009
Pullback and forward attractors for a damped wave equation with delays. Zbl 1061.35153
Caraballo, T.; Kloeden, P. E.; Real, J.
2004
Pathwise approximation of stochastic differential equations on domains: Higher order convergence rates without global Lipschitz coefficients. Zbl 1163.65003
Jentzen, A.; Kloeden, P. E.; Neuenkirch, A.
2009
Remarks on Peano-like theorems for fuzzy differential equations. Zbl 0742.34058
Kloeden, P. E.
1991
Pullback attractors of nonautonomous semidynamical systems. Zbl 1029.37010
Kloeden, P. E.
2003
Stratonovich and Itô stochastic Taylor expansions. Zbl 0731.60050
Kloeden, P. E.; Platen, E.
1991
Compact supported endographs and fuzzy sets. Zbl 0441.54008
Kloeden, P. E.
1980
On Sharkovsky’s cycle coexistence ordering. Zbl 0465.58022
Kloeden, Peter E.
1979
Efficient simulation of nonlinear parabolic SPDEs with additive noise. Zbl 1223.60050
Jentzen, Arnulf; Kloeden, Peter; Winkel, Georg
2011
Cocycle attractors in nonautonomously perturbed differential equations. Zbl 0905.34047
Kloeden, P. E.; Stonier, D. J.
1998
Synchronization of a stochastic reaction-diffusion system on a thin two-layer domain. Zbl 1125.37058
Caraballo, Tomás; Chueshov, Igor D.; Kloeden, Peter E.
2007
Mean-square random dynamical systems. Zbl 1267.37018
Kloeden, Peter E.; Lorenz, Thomas
2012
The approximation of multiple stochastic integrals. Zbl 0761.60048
Kloeden, P. E.; Platen, E.; Wright, I. W.
1992
Pullback attractors in nonautonomous difference equations. Zbl 0961.39007
Kloeden, Peter E.
2000
Unique strong solutions and $$V$$-attractors of a three dimensional system of globally modified Navier-Stokes equations. Zbl 1220.35115
Caraballo, Tomás; Real, José; Kloeden, Peter E.
2006
Random attractors of stochastic reaction-diffusion equations on variable domains. Zbl 1235.60076
Crauel, H.; Kloeden, P. E.; Yang, Meihua
2011
The exponential integrator scheme for stochastic partial differential equations: Pathwise error bounds. Zbl 1208.65017
Kloeden, P. E.; Lord, G. J.; Neuenkirch, A.; Shardlow, T.
2011
Asymptotic invariance and limit sets of general control systems. Zbl 0306.93024
Kloeden, P. E.
1975
Random attractors for stochastic semi-linear degenerate parabolic equations. Zbl 1222.35042
Yang, Meihua; Kloeden, P. E.
2011
Pullback attractors for a semilinear heat equation on time-varying domains. Zbl 1173.37064
Kloeden, Peter E.; Real, José; Sun, Chunyou
2009
Linear-implicit strong schemes for Itô-Galerkin approximations of stochastic PDEs. Zbl 0988.60066
Kloeden, P. E.; Shott, S.
2001
Anisotropy-based robust performance analysis of finite horizon linear discrete time varying systems. Zbl 1194.93052
Vladimirov, I. G.; Diamond, P.; Kloeden, P.
2006
Pullback attractors for a semilinear heat equation in a non-cylindrical domain. Zbl 1146.35016
Kloeden, P. E.; Marín-Rubio, P.; Real, J.
2008
Taylor expansions of solutions of stochastic partial differential equations with additive noise. Zbl 1220.35202
Jentzen, Arnulf; Kloeden, Peter
2010
Bifurcations and continuous transitions of attractors in autonomous and nonautonomous systems. Zbl 1079.34041
Kloeden, P. E.; Siegmund, S.
2005
Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations. Zbl 1283.60098
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
2013
Pullback attractors in dissipative nonautonomous differential equations under discretization. Zbl 0999.34054
Cheban, D. N.; Kloeden, P. E.; Schmalfuß, B.
2001
The persistence of synchronization under environmental noise. Zbl 1206.60054
Caraballo, Tomás; Kloeden, Peter E.
2005
Construction of nonautonomous forward attractors. Zbl 1362.37045
Kloeden, Peter E.; Lorenz, Thomas
2016
Global existence of classical solutions in the dissipative shallow water equations. Zbl 0579.76047
Kloeden, P. E.
1985
Non-autonomous lattice systems with switching effects and delayed recovery. Zbl 1345.34128
Han, Xiaoying; Kloeden, Peter E.
2016
Nonautonomous and random attractors. Zbl 1358.37041
Crauel, Hans; Kloeden, Peter E.
2015
Discretization of stationary solutions of stochastic systems driven by fractional Brownian motion. Zbl 1180.93095
Garrido-Atienza, María J.; Kloeden, Peter E.; Neuenkirch, Andreas
2009
Invariant measures and statistical solutions of the globally modified Navier-Stokes equations. Zbl 1187.35152
Caraballo, Tomás; Kloeden, Peter E.; Real, José
2008
Stochastic differential equations with nonlocal sample dependence. Zbl 1205.60131
Kloeden, Peter E.; Lorenz, Thomas
2010
Mean-square random attractors of stochastic delay differential equations with random delay. Zbl 1316.34083
Wu, Fuke; Kloeden, Peter E.
2013
Pathwise approximation of random ordinary differential equations. Zbl 0998.65010
Grüne, L.; Kloeden, P. E.
2001
Attractors of asymptotically autonomous quasi-linear parabolic equation with spatially variable exponents. Zbl 1310.35203
Kloeden, Peter E.; Simsen, Jacson
2015
Equivalence of invariant measures and stationary statistical solutions for the autonomous globally modified Navier-Stokes equations. Zbl 1168.35412
Kloeden, P. E.; Marín-Rubio, Pedro; Real, José
2009
The weak connectedness of the attainability set of weak solutions of the three-dimensional Navier-Stokes equations. Zbl 1143.35082
Kloeden, P. E.; Valero, J.
2007
Asymptotic behavior of solutions for random wave equations with nonlinear damping and white noise. Zbl 1202.35124
Yang, Meihua; Duan, Jinqiao; Kloeden, Peter
2011
The uniform attractor of a multi-valued process generated by reaction-diffusion delay equations on an unbounded domain. Zbl 1304.35738
Wang, Yejuan; Kloeden, Peter E.
2014
Pullback attractors for non-autonomous quasi-linear parabolic equations with dynamical boundary conditions. Zbl 1261.37033
Yang, Lu; Yang, Meihua; Kloeden, Peter E.
2012
Two-step transition in nonautonomous bifurcations: An explanation. Zbl 1009.34037
Johnson, R. A.; Kloeden, P. E.; Pavani, R.
2002
Higher order numerical schemes for affinely controlled nonlinear systems. Zbl 0992.65075
Grüne, L.; Kloeden, P. E.
2001
Asymptotic behavior of stochastic lattice systems with a Caputo fractional time derivative. Zbl 1337.26021
Wang, Yejuan; Xu, Jiaohui; Kloeden, Peter E.
2016
The Milstein scheme for stochastic delay differential equations without using anticipative calculus. Zbl 1247.65005
Kloeden, P. E.; Shardlow, T.
2012
Random ordinary differential equations and their numerical solution. Zbl 1392.60003
Han, Xiaoying; Kloeden, Peter E.
2017
Weak pullback attractors of setvalued processes. Zbl 1044.93035
Caraballo, T.; Kloeden, P. E.; Marín-Rubio, P.
2003
Asymptotically autonomous multivalued Cauchy problems with spatially variable exponents. Zbl 1349.35443
Kloeden, Peter E.; Simsen, Jacson; Stefanello Simsen, Mariza
2017
Pathwise convergent higher order numerical schemes for random ordinary differential equations. Zbl 1140.65015
Kloeden, Peter E.; Jentzen, Arnulf
2007
Pullback attractors for non-autonomous evolution equations with spatially variable exponents. Zbl 1304.35120
Kloeden, Peter E.; Simsen, Jacson
2014
Discrete-time nonautonomous dynamical systems. Zbl 1310.37011
Kloeden, P. E.; Pötzsche, C.; Rasmussen, M.
2013
Chaotic iterations of fuzzy sets. Zbl 0746.54010
Kloeden, P. E.
1991
The inflation of attractors and their discretization: The autonomous case. Zbl 0958.37006
Kloeden, P. E.; Kozyakin, V. S.
2000
Nonautonomous attractors of switching systems. Zbl 1136.37313
Kloeden, P. E.
2006
On the asymptotical behavior of nonautonomous dynamical systems. Zbl 1134.34319
Wang, Yejuan; Li, Desheng; Kloeden, P. E.
2004
Pathwise upper semi-continuity of random pullback attractors along the time axis. Zbl 1392.37042
Cui, Hongyong; Kloeden, Peter E.; Wu, Fuke
2018
The numerical solution of stochastic differential equations. Zbl 0359.60081
Kloeden, P. E.; Pearson, R. A.
1977
Metric topology of fuzzy numbers and fuzzy analysis. Zbl 0988.26019
Diamond, Phil; Kloeden, Peter
2000
Li–Yorke chaos in higher dimensions: a review. Zbl 1096.39019
Kloeden, Peter; Li, Zhong
2006
Pullback $$V$$-attractors of the 3-dimensional globally modified Navier-Stokes equations. Zbl 1152.35086
Kloeden, Peter E.; Langa, José A.; Real, José
2007
Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations. Zbl 1270.65005
Wu, Fuke; Mao, Xuerong; Kloeden, Peter E.
2013
On effects of discretization on estimators of drift parameters for diffusion processes. Zbl 0873.65134
Kloeden, P. E.; Platen, E.; Schurz, H.; Sørensen, M.
1996
On the dynamics of nonautonomous periodic general dynamical systems and differential inclusions. Zbl 1091.37007
Li, Desheng; Kloeden, Peter E.
2006
Nonautonomous chemostats with variable delays. Zbl 1323.92155
Caraballo, Tomás; Han, Xiaoying; Kloeden, Peter E.
2015
Asymptotic behavior of a nonautonomous $$p$$-Laplacian lattice system. Zbl 1352.34014
Gu, Anhui; Kloeden, Peter E.
2016
Pathwise Taylor schemes for random ordinary differential equations. Zbl 1162.65305
Jentzen, Arnulf; Kloeden, Peter E.
2009
A note on the Euler-Maruyama scheme for stochastic differential equations with a discontinuous monotone drift coefficient. Zbl 1136.65008
Halidias, Nikolaos; Kloeden, Peter E.
2008
Dynamics of a class of ODEs more general than almost periodic. Zbl 1217.34101
Kloeden, P. E.; Rodrigues, H. M.
2011
Convergence of numerical methods for stochastic differential equations in mathematical finance. Zbl 1277.91194
Kloeden, Peter; Neuenkirch, Andreas
2013
Sigmoidal approximations of Heaviside functions in neural lattice models. Zbl 1434.34023
Han, Xiaoying; Kloeden, Peter E.
2020
Strong $$(L^2,L^\gamma\cap H_0^1)$$-continuity in initial data of nonlinear reaction-diffusion equation in any space dimension. Zbl 1448.35298
Cui, Hongyong; Kloeden, Peter E.; Zhao, Wenqiang
2020
The truncated Euler-Maruyama method for stochastic differential equations with Hölder diffusion coefficients. Zbl 07126160
Yang, Hao; Wu, Fuke; Kloeden, Peter E.; Mao, Xuerong
2020
Attractors of Hopfield-type lattice models with increasing neuronal input. Zbl 1432.34020
Wang, Xiaoli; Kloeden, Peter E.; Han, Xiaoying
2020
A free boundary tumor model with time dependent nutritional supply. Zbl 1433.35431
Sun, Wenlong; Caraballo, Tomás; Han, Xiaoying; Kloeden, Peter E.
2020
Random recurrent neural networks with delays. Zbl 1453.34105
Sui, Meiyu; Wang, Yejuan; Han, Xiaoying; Kloeden, Peter E.
2020
Asymptotic behaviour of a neural field lattice model with delays. Zbl 1447.34068
Wang, Xiaoli; Kloeden, Peter; Yang, Meihua
2020
Sigmoidal approximations of a delay neural lattice model with heaviside functions. Zbl 1451.34101
Wang, Xiaoli; Yang, Meihua; Kloeden, Peter E.
2020
Asymptotic behavior of a neural field lattice model with a heaviside operator. Zbl 1448.82025
Han, Xiaoying; Kloeden, Peter E.
2019
Long term behavior of a random Hopfield neural lattice model. Zbl 1404.37093
Han, Xiaoying; Kloeden, Peter E.; Usman, Basiru
2019
Lattice dynamical systems in the biological sciences. Zbl 1427.92043
Han, Xiaoying; Kloeden, Peter E.
2019
Tail convergences of pullback attractors for asymptotically converging multi-valued dynamical systems. Zbl 1416.37019
Cui, Hongyong; Kloeden, Peter E.
2019
Forward attracting sets of reaction-diffusion equations on variable domains. Zbl 1409.37077
Kloeden, Peter E.; Yang, Meihua
2019
Existence and approximation of strong solutions of SDEs with fractional diffusion coefficients. Zbl 1420.60076
Yang, Hao; Wu, Fuke; Kloeden, Peter E.
2019
Pathwise upper semi-continuity of random pullback attractors along the time axis. Zbl 1392.37042
Cui, Hongyong; Kloeden, Peter E.; Wu, Fuke
2018
Invariant forward attractors of non-autonomous random dynamical systems. Zbl 1408.37036
Cui, Hongyong; Kloeden, Peter E.
2018
Asymptotic separation between solutions of Caputo fractional stochastic differential equations. Zbl 1401.26009
Dr. Son, Doan Thai; Huong, Phan Thi; Kloeden, Peter E.; Tuan, Hoang The
2018
Long term dynamics of second order-in-time stochastic evolution equations with state-dependent delay. Zbl 1395.60070
Chueshov, Igor; Kloeden, Peter E.; Yang, Meihua
2018
Random ordinary differential equations and their numerical solution. Zbl 1392.60003
Han, Xiaoying; Kloeden, Peter E.
2017
Asymptotically autonomous multivalued Cauchy problems with spatially variable exponents. Zbl 1349.35443
Kloeden, Peter E.; Simsen, Jacson; Stefanello Simsen, Mariza
2017
Gauss-quadrature method for one-dimensional mean-field SDEs. Zbl 1378.65035
Kloeden, Peter; Shardlow, Tony
2017
Pullback attractors of reaction-diffusion inclusions with space-dependent delay. Zbl 1359.35015
Lorenz, Thomas; Kloeden, Peter E.
2017
Attractors under discretisation. Zbl 1381.65099
Han, Xiaoying; Kloeden, Peter
2017
Global exponential $$\kappa$$-dissipative semigroups and exponential attraction. Zbl 1367.47062
Zhang, Jin; Kloeden, Peter E.; Yang, Meihua; Zhong, Chengkui
2017
Impulsive fractional functional differential equations with a weakly continuous nonlinearity. Zbl 1386.34132
Wang, Yejuan; Gao, Fengshuang; Kloeden, Peter
2017
Construction of nonautonomous forward attractors. Zbl 1362.37045
Kloeden, Peter E.; Lorenz, Thomas
2016
Non-autonomous lattice systems with switching effects and delayed recovery. Zbl 1345.34128
Han, Xiaoying; Kloeden, Peter E.
2016
Asymptotic behavior of stochastic lattice systems with a Caputo fractional time derivative. Zbl 1337.26021
Wang, Yejuan; Xu, Jiaohui; Kloeden, Peter E.
2016
Asymptotic behavior of a nonautonomous $$p$$-Laplacian lattice system. Zbl 1352.34014
Gu, Anhui; Kloeden, Peter E.
2016
An exponential Wagner-Platen type scheme for SPDEs. Zbl 1345.60068
Becker, Sebastian; Jentzen, Arnulf; Kloeden, Peter E.
2016
Multi-step methods for random ODEs driven by Itô diffusions. Zbl 1327.34109
Asai, Y.; Kloeden, P. E.
2016
Asymptotic invariance and the discretisation of nonautonomous forward attracting sets. Zbl 1366.34082
Kloeden, Peter E.
2016
Nonlocal multi-scale traffic flow models: analysis beyond vector spaces. Zbl 1362.35184
Kloeden, Peter E.; Lorenz, Thomas
2016
A nonlocal sample dependence SDE-PDE system modeling proton dynamics in a tumor. Zbl 1347.60086
Kloeden, Peter E.; Sonner, Stefanie; Surulescu, Christina
2016
Forward attractors in discrete time nonautonomous dynamical systems. Zbl 1375.37052
Kloeden, Peter E.; Lorenz, Thomas; Yang, Meihua
2016
Synchronization in coupled stochastic sine-Gordon wave model. Zbl 1352.37187
Chueshov, Igor; Kloeden, Peter E.; Yang, Meihua
2016
Numerical schemes for random ODEs with affine noise. Zbl 1357.65009
Asai, Y.; Kloeden, P. E.
2016
Nonautonomous and random attractors. Zbl 1358.37041
Crauel, Hans; Kloeden, Peter E.
2015
Attractors of asymptotically autonomous quasi-linear parabolic equation with spatially variable exponents. Zbl 1310.35203
Kloeden, Peter E.; Simsen, Jacson
2015
Nonautonomous chemostats with variable delays. Zbl 1323.92155
Caraballo, Tomás; Han, Xiaoying; Kloeden, Peter E.
2015
Chemostats with random inputs and wall growth. Zbl 1341.34053
Caraballo, Tomás; Han, Xiaoying; Kloeden, Peter E.
2015
The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor. Zbl 1366.37122
Doan, Thai Son; Rasmussen, Martin; Kloeden, Peter E.
2015
A Peano theorem for fuzzy differential equations with evolving membership grade. Zbl 1377.34003
Kloeden, Peter E.; Lorenz, Thomas
2015
Dynamics of nonautonomous chemostat models. Zbl 1335.92062
Caraballo, Tomás; Han, Xiaoying; Kloeden, Peter E.; Rapaport, Alain
2015
Nonautonomous bifurcation scenarios in SIR models. Zbl 1357.37090
Kloeden, P. E.; Pötzsche, C.
2015
Pullback and forward attractors of nonautonomous difference equations. Zbl 1336.39014
Kloeden, Peter; Lorenz, Thomas
2015
The uniform attractor of a multi-valued process generated by reaction-diffusion delay equations on an unbounded domain. Zbl 1304.35738
Wang, Yejuan; Kloeden, Peter E.
2014
Pullback attractors for non-autonomous evolution equations with spatially variable exponents. Zbl 1304.35120
Kloeden, Peter E.; Simsen, Jacson
2014
Pullback incremental attraction. Zbl 1308.37009
Kloeden, Peter E.; Lorenz, Thomas
2014
Asymptotic behaviour of the nonautonomous SIR equations with diffusion. Zbl 1272.35043
Anguiano, María; Kloeden, P. E.
2014
Reaction-diffusion equations with a switched-off reaction zone. Zbl 1304.35791
Kloeden, Peter E.; Lorenz, Thomas; Yang, Meihua
2014
Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations. Zbl 1283.60098
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
2013
Mean-square random attractors of stochastic delay differential equations with random delay. Zbl 1316.34083
Wu, Fuke; Kloeden, Peter E.
2013
Discrete-time nonautonomous dynamical systems. Zbl 1310.37011
Kloeden, P. E.; Pötzsche, C.; Rasmussen, M.
2013
Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations. Zbl 1270.65005
Wu, Fuke; Mao, Xuerong; Kloeden, Peter E.
2013
Convergence of numerical methods for stochastic differential equations in mathematical finance. Zbl 1277.91194
Kloeden, Peter; Neuenkirch, Andreas
2013
Fuzzy differential equations without fuzzy convexity. Zbl 1314.34011
Kloeden, Peter E.; Lorenz, Thomas
2013
Nonautonomous dynamical systems in the life sciences. Zbl 1311.37075
Kloeden, Peter E.; Pötzsche, Christian
2013
Numerical schemes for random ODEs via stochastic differential equations. Zbl 1294.60091
Asai, Y.; Kloeden, P. E.
2013
Pullback attractors of a multi-valued process generated by parabolic differential equations with unbounded delays. Zbl 1282.35398
Wang, Yejuan; Kloeden, P. E.
2013
The three-dimensional globally modified Navier-Stokes equations: recent developments. Zbl 1317.76030
Caraballo, T.; Kloeden, P. E.
2013
Stable integration of stiff random ordinary differential equations. Zbl 1273.60079
Asai, Y.; Herrmann, E.; Kloeden, P. E.
2013
A Peano-like theorem for stochastic differential equations with nonlocal sample dependence. Zbl 1273.60081
Kloeden, Peter E.; Lorenz, Thomas
2013
Switching systems and entropy. Zbl 1373.37046
Amigó, José M.; Kloeden, Peter E.; Giménez, Ángel
2013
Entropy increase in switching systems. Zbl 1310.37009
Amigó, José M.; Kloeden, Peter E.; Giménez, Ángel
2013
Recent developments in computational finance. Foundations, algorithms and applications. In part based on the presentations at the international workshop on numerical algorithms in computational finance, Frankfurt/Main, Germany, July 20–22, 2011. Zbl 1272.91008
Gerstner, Thomas; Kloeden, Peter
2013
The envelope attractor of non-strict multivalued dynamical systems with application to the 3D Navier-Stokes and reaction-diffusion equations. Zbl 1277.35066
Kloeden, P. E.; Marín-Rubio, P.; Valero, J.
2013
Asymptotic behaviour of random tridiagonal Markov chains in biological applications. Zbl 1277.60118
Kloeden, Peter E.; Kozyakin, Victor
2013
Nonautonomous dynamical systems in the life sciences. Zbl 1282.37004
Kloeden, Peter E.; Pötzsche, Christian
2013
Asymptotic behaviour of random Markov chains with tridiagonal generators. Zbl 1268.34105
Kloeden, Peter E.; Kozyakin, Victor S.
2013
Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients. Zbl 1256.65003
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
2012
Mean-square random dynamical systems. Zbl 1267.37018
Kloeden, Peter E.; Lorenz, Thomas
2012
Pullback attractors for non-autonomous quasi-linear parabolic equations with dynamical boundary conditions. Zbl 1261.37033
Yang, Lu; Yang, Meihua; Kloeden, Peter E.
2012
The Milstein scheme for stochastic delay differential equations without using anticipative calculus. Zbl 1247.65005
Kloeden, P. E.; Shardlow, T.
2012
Limitations of pullback attractors for processes. Zbl 1241.39004
Kloeden, Peter E.; Pötzsche, Christian; Rasmussen, Martin
2012
Diamond, Phil; Kloeden, Peter; Kozyakin, Victor; Pokrovskii, Alexei
2012
Strong and weak divergence in finite time of Euler’s method for stochastic differential equations with non-globally Lipschitz continuous coefficients. Zbl 1228.65014
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
2011
Nonautonomous dynamical systems. Zbl 1244.37001
Kloeden, Peter E.; Rasmussen, Martin
2011
Taylor approximations for stochastic partial differential equations. Zbl 1240.35001
Jentzen, Arnulf; Kloeden, Peter
2011
Efficient simulation of nonlinear parabolic SPDEs with additive noise. Zbl 1223.60050
Jentzen, Arnulf; Kloeden, Peter; Winkel, Georg
2011
Random attractors of stochastic reaction-diffusion equations on variable domains. Zbl 1235.60076
Crauel, H.; Kloeden, P. E.; Yang, Meihua
2011
The exponential integrator scheme for stochastic partial differential equations: Pathwise error bounds. Zbl 1208.65017
Kloeden, P. E.; Lord, G. J.; Neuenkirch, A.; Shardlow, T.
2011
Random attractors for stochastic semi-linear degenerate parabolic equations. Zbl 1222.35042
Yang, Meihua; Kloeden, P. E.
2011
Asymptotic behavior of solutions for random wave equations with nonlinear damping and white noise. Zbl 1202.35124
Yang, Meihua; Duan, Jinqiao; Kloeden, Peter
2011
Dynamics of a class of ODEs more general than almost periodic. Zbl 1217.34101
Kloeden, P. E.; Rodrigues, H. M.
2011
Almost sure exponential stability of the Euler-Maruyama approximations for stochastic functional differential equations. Zbl 1276.60063
Wu, Fuke; Mao, Xuerong; Kloeden, Peter E.
2011
Robust exponential attractors for non-autonomous equations with memory. Zbl 1229.35134
Kloeden, Peter E.; Real, José; Sun, Chunyou
2011
Negatively invariant sets and entire trajectories of set-valued dynamical systems. Zbl 1225.37022
Kloeden, Peter E.; Marín-Rubio, Pedro
2011
Multilevel Monte Carlo for stochastic differential equations with additive fractional noise. Zbl 1235.60064
Kloeden, Peter E.; Neuenkirch, Andreas; Pavani, Raffaella
2011
Stochastic morphological evolution equations. Zbl 1230.35149
Kloeden, Peter E.; Lorenz, Thomas
2011
The numerical stability of stochastic ordinary differential equations with additive noise. Zbl 1236.60067
Buckwar, E.; Riedler, M. G.; Kloeden, P. E.
2011
Negatively invariant sets and entire solutions. Zbl 1228.37014
Kloeden, Peter E.; Marín-Rubio, Pedro
2011
The dynamics of epidemiological systems with nonautonomous and random coefficients. Zbl 1215.37016
Kloeden, Peter E.; Kozyakin, Victor S.
2011
Recent developments in dynamical systems: three perspectives. Zbl 1202.37003
Balibrea, F.; Caraballo, T.; Kloeden, P. E.; Valero, J.
2010
Numerical solution of stochastic differential equations. 4th corrected printing. Zbl 1216.60052
Kloeden, Peter E.; Platen, Eckhard
2010
Taylor expansions of solutions of stochastic partial differential equations with additive noise. Zbl 1220.35202
Jentzen, Arnulf; Kloeden, Peter
2010
Stochastic differential equations with nonlocal sample dependence. Zbl 1205.60131
Kloeden, Peter E.; Lorenz, Thomas
2010
Synchronization of systems of Marcus canonical equations driven by $$\alpha$$-stable noises. Zbl 1203.37124
Liu, Xianming; Duan, Jinqiao; Liu, Jicheng; Kloeden, Peter E.
2010
Stochastic partial differential equations with additive noise on time-varying domains. Zbl 1242.60063
Crauel, Hans; Kloeden, Peter E.; Real Anguas, José
2010
Synchronization of dissipative dynamical systems driven by non-Gaussian Lévy noises. Zbl 1218.60051
Liu, Xianming; Duan, Jinqiao; Liu, Jicheng; Kloeden, Peter E.
2010
...and 210 more Documents
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#### Cited by 4,437 Authors

 174 Kloeden, Peter Eris 76 Caraballo Garrido, Tomás 46 Mao, Xuerong 46 Wang, Bixiang 43 Li, Yangrong 37 Langa, Jose’ Antonio 36 Jentzen, Arnulf 29 Duan, Jinqiao 28 Gan, Siqing 27 Han, Xiaoying 27 Wang, Yejuan 26 Diamond, Phil 26 Wang, Xiaojie 25 Burrage, Kevin 25 Marín-Rubio, Pedro 25 Valero, José 25 Zhou, Shengfan 21 Allen, Edward James 21 Neuenkirch, Andreas 21 Rößler, Andreas 20 Real Anguas, José 20 Wang, Renhai 19 Jimenez, Juan Carlos 18 Khastan, Alireza 18 Li, Desheng 18 Platen, Eckhard 18 Rasmussen, Martin 18 Schmalfuß, Björn 18 Tachim Medjo, Theodore 18 Wu, Congxin 18 Yuan, Chenggui 17 Cortés López, Juan Carlos 17 Müller-Gronbach, Thomas 17 Nolasco de Carvalho, Alexandre 17 Pokrovskiĭ, Alexeĭ Vadimovich 16 Buckwar, Evelyn 16 Cui, Hongyong 16 Debrabant, Kristian 16 Gu, Anhui 16 Lorenz, Thomas 16 Wu, Fuke 16 Yang, Meihua 15 Huang, Chengming 15 Łukaszewicz, Grzegorz 15 Nieto Roig, Juan Jose 15 Sun, Chunyou 15 Zhao, Caidi 14 Colubi, Ana 14 Coroianu, Lucian C. 14 Gong, Zengtai 14 Lu, Kening 14 Przybyłowicz, Paweł 14 Robinson, James Cooper 14 Simsen, Jacson 13 Anguiano, María 13 Chalco-Cano, Yurilev 13 Gil, María Angeles 13 Higham, Desmond J. 13 Hong, Jialin 13 Hosseini, Seyed Mohammad 13 Kurdyukov, Alexander P. 13 Kuznetsov, Dmitriĭ Feliksovich 13 Li, Dingshi 13 Rodríguez-López, Rosana 13 Tocino, Alicia 13 Zaslavski, Alexander Yakovlevich 13 Zhang, Qimin 12 Garrido-Atienza, María José 12 Malinowski, Marek T. 12 Zhao, Weidong 11 Allahviranloo, Tofigh 11 Colucci, Renato 11 Ding, Xiaohua 11 Kasyanov, Pavlo O. 11 Ma, Qiang 11 Roberts, Gareth O. 11 Román-Flores, Heriberto E. 11 Savaş, Ekrem 10 Feng, Yuhu 10 Huang, Huan 10 Huang, Jianhua 10 Hutzenthaler, Martin 10 Liu, Wei 10 Ma, Qiaozhen 10 Ngo, Hoang-Long 10 Pötzsche, Christian 10 Qiu, Dong 10 Sabanis, Sotirios 10 Stuart, Andrew M. 10 Syau, Yu-Ru 10 Szpruch, Lukasz 10 Tambue, Antoine 10 Wang, Xiaohu 10 Wang, Zhaojuan 10 Yamada, Toshihiro 10 You, Bo 9 Atzberger, Paul J. 9 Burrage, Pamela M. 9 Carbonell, Felix 9 D’Ambrosio, Raffaele ...and 4,337 more Authors
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#### Cited in 478 Serials

 218 Fuzzy Sets and Systems 194 Journal of Computational and Applied Mathematics 133 Applied Mathematics and Computation 116 Journal of Mathematical Analysis and Applications 114 Journal of Differential Equations 110 Discrete and Continuous Dynamical Systems. Series B 97 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 85 Journal of Computational Physics 83 Stochastic Analysis and Applications 72 Applied Numerical Mathematics 65 Computers & Mathematics with Applications 58 BIT 53 Stochastics and Dynamics 49 Stochastic Processes and their Applications 48 Information Sciences 47 Abstract and Applied Analysis 45 Mathematics and Computers in Simulation 45 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 45 Journal of Difference Equations and Applications 45 Discrete and Continuous Dynamical Systems 43 The Annals of Applied Probability 40 Advances in Difference Equations 36 Applied Mathematical Modelling 35 Numerical Algorithms 34 SIAM Journal on Numerical Analysis 33 Journal of Mathematical Physics 32 Physica D 32 Communications on Pure and Applied Analysis 31 Nonlinear Analysis. Real World Applications 30 Soft Computing 28 International Journal of Computer Mathematics 27 Mathematics of Computation 27 Automation and Remote Control 27 Journal of Dynamics and Differential Equations 26 Chaos 25 Journal of Statistical Physics 25 Statistics & Probability Letters 25 Communications in Nonlinear Science and Numerical Simulation 23 Mathematical Problems in Engineering 22 Automatica 21 Monte Carlo Methods and Applications 21 Nonlinear Dynamics 20 Chaos, Solitons and Fractals 20 Journal of Econometrics 20 Applied Mathematics Letters 19 Systems & Control Letters 18 Numerische Mathematik 18 Computational Statistics and Data Analysis 18 Journal of Theoretical Biology 17 Computer Physics Communications 17 Journal of Complexity 17 Mathematical and Computer Modelling 17 SIAM Journal on Scientific Computing 16 Journal of Mathematical Biology 16 Mathematical Biosciences 16 Differentsial’nye Uravneniya i Protsessy Upravleniya 16 SIAM/ASA Journal on Uncertainty Quantification 16 Nonlinear Analysis. Theory, Methods & Applications 15 Journal of Scientific Computing 15 Multiscale Modeling & Simulation 14 Applicable Analysis 14 Journal of Applied Analysis and Computation 14 Stochastic and Partial Differential Equations. Analysis and Computations 13 Proceedings of the American Mathematical Society 13 International Journal of Approximate Reasoning 13 Journal of Nonlinear Science 12 Nonlinearity 12 Discrete Dynamics in Nature and Society 12 Journal of Applied Mathematics and Computing 11 Journal of Fluid Mechanics 11 Mathematical Methods in the Applied Sciences 11 Bulletin of Mathematical Biology 11 Journal of Applied Probability 11 Numerical Functional Analysis and Optimization 11 Computational and Applied Mathematics 11 Finance and Stochastics 11 Dynamical Systems 11 Journal of Applied Mathematics 11 Statistics and Computing 10 Computer Methods in Applied Mechanics and Engineering 10 The Annals of Probability 10 Transactions of the American Mathematical Society 10 Journal of Economic Dynamics & Control 10 European Journal of Operational Research 10 Mathematical Biosciences and Engineering 10 Stochastics 10 Discrete and Continuous Dynamical Systems. Series S 10 Set-Valued and Variational Analysis 9 Physica A 9 Physics Letters. A 9 Applied Mathematics and Optimization 9 Insurance Mathematics & Economics 9 Differential Equations and Dynamical Systems 9 Methodology and Computing in Applied Probability 9 Nonlinear Analysis. Hybrid Systems 8 International Journal of General Systems 8 Journal of Optimization Theory and Applications 8 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 8 Bernoulli 8 Boundary Value Problems ...and 378 more Serials
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#### Cited in 57 Fields

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