July  2015, 20(5): i-ii. doi: 10.3934/dcdsb.2015.20.5i

Special section on differential equations: Theory, application, and numerical approximation

1. 

Department of Mathematics & Statistics, Auburn University, Auburn, AL 36849

2. 

School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, China

3. 

Beijing Computational Science Research Center, Beijing 100084, China

Published  May 2015

It is our honor to bring you this special section dedicated to recent advances in computational and applied mathematics in science and engineering. These articles comprise a collection of diverse theoretical results as well as applications, primarily centered on the following areas.

For more information please click the “Full Text” above.
Citation: Yanzhao Cao, Anping Liu, Zhimin Zhang. Special section on differential equations: Theory, application, and numerical approximation. Discrete and Continuous Dynamical Systems - B, 2015, 20 (5) : i-ii. doi: 10.3934/dcdsb.2015.20.5i
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Leon Petrosyan, David Yeung. Shapley value for differential network games: Theory and application. Journal of Dynamics and Games, 2021, 8 (2) : 151-166. doi: 10.3934/jdg.2020021

[2]

Arnaud Münch, Ademir Fernando Pazoto. Boundary stabilization of a nonlinear shallow beam: theory and numerical approximation. Discrete and Continuous Dynamical Systems - B, 2008, 10 (1) : 197-219. doi: 10.3934/dcdsb.2008.10.197

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Runzhang Xu. Preface: Special issue on advances in partial differential equations. Discrete and Continuous Dynamical Systems - S, 2021, 14 (12) : i-i. doi: 10.3934/dcdss.2021137

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Ulrike Kant, Werner M. Seiler. Singularities in the geometric theory of differential equations. Conference Publications, 2011, 2011 (Special) : 784-793. doi: 10.3934/proc.2011.2011.784

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Youssef El Hadfi, Zhaosheng Feng, Abdelghani Ghazdali, Amine Laghrib. Preface to the special issue "Partial Differential Equations, Optimization and their Applications". Discrete and Continuous Dynamical Systems - S, 2022, 15 (1) : i-ii. doi: 10.3934/dcdss.2021163

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Wilhelm Schlag. Spectral theory and nonlinear partial differential equations: A survey. Discrete and Continuous Dynamical Systems, 2006, 15 (3) : 703-723. doi: 10.3934/dcds.2006.15.703

[7]

Nicola Guglielmi, Christian Lubich. Numerical periodic orbits of neutral delay differential equations. Discrete and Continuous Dynamical Systems, 2005, 13 (4) : 1057-1067. doi: 10.3934/dcds.2005.13.1057

[8]

Joseph D. Fehribach. Using numerical experiments to discover theorems in differential equations. Discrete and Continuous Dynamical Systems - B, 2003, 3 (4) : 495-504. doi: 10.3934/dcdsb.2003.3.495

[9]

Roberto Garrappa, Eleonora Messina, Antonia Vecchio. Effect of perturbation in the numerical solution of fractional differential equations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (7) : 2679-2694. doi: 10.3934/dcdsb.2017188

[10]

Joseph A. Connolly, Neville J. Ford. Comparison of numerical methods for fractional differential equations. Communications on Pure and Applied Analysis, 2006, 5 (2) : 289-307. doi: 10.3934/cpaa.2006.5.289

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Badam Ulemj, Enkhbat Rentsen, Batchimeg Tsendpurev. Application of survival theory in taxation. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2573-2578. doi: 10.3934/jimo.2020083

[12]

Chuchu Chen, Jialin Hong, Yulan Lu. Stochastic differential equation with piecewise continuous arguments: Markov property, invariant measure and numerical approximation. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022098

[13]

Pierre Magal. Global stability for differential equations with homogeneous nonlinearity and application to population dynamics. Discrete and Continuous Dynamical Systems - B, 2002, 2 (4) : 541-560. doi: 10.3934/dcdsb.2002.2.541

[14]

Roman Srzednicki. A theorem on chaotic dynamics and its application to differential delay equations. Conference Publications, 2001, 2001 (Special) : 362-365. doi: 10.3934/proc.2001.2001.362

[15]

Yanmin Niu, Xiong Li. An application of Moser's twist theorem to superlinear impulsive differential equations. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 431-445. doi: 10.3934/dcds.2019017

[16]

Ali Hamidoǧlu. On general form of the Tanh method and its application to nonlinear partial differential equations. Numerical Algebra, Control and Optimization, 2016, 6 (2) : 175-181. doi: 10.3934/naco.2016007

[17]

Xianming Liu, Guangyue Han. A Wong-Zakai approximation of stochastic differential equations driven by a general semimartingale. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2499-2508. doi: 10.3934/dcdsb.2020192

[18]

Burcu Gürbüz. A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering. Journal of Industrial and Management Optimization, 2022, 18 (4) : 2319-2334. doi: 10.3934/jimo.2021069

[19]

Carmen Núñez, Rafael Obaya. A non-autonomous bifurcation theory for deterministic scalar differential equations. Discrete and Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 701-730. doi: 10.3934/dcdsb.2008.9.701

[20]

Qi Lü, Xu Zhang. A concise introduction to control theory for stochastic partial differential equations. Mathematical Control and Related Fields, 2021  doi: 10.3934/mcrf.2021020

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