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 & Continuous Dynamical Systems - B, 2015, 20 (5) : i-ii. doi: 10.3934/dcdsb.2015.20.5i
[1]

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

[2]

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

[3]

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

[4]

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

[5]

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

[6]

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

[7]

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

[8]

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

[9]

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

[10]

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

[11]

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

[12]

Ping Liu, Ying Su, Fengqi Yi. Preface for special session entitled "Recent Advances of Differential Equations with Applications in Life Sciences". Discrete & Continuous Dynamical Systems - S, 2017, 10 (5) : i-i. doi: 10.3934/dcdss.201705i

[13]

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

[14]

Yuhki Hosoya. First-order partial differential equations and consumer theory. Discrete & Continuous Dynamical Systems - S, 2018, 11 (6) : 1143-1167. doi: 10.3934/dcdss.2018065

[15]

Nikolaos Halidias. Construction of positivity preserving numerical schemes for some multidimensional stochastic differential equations. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 153-160. doi: 10.3934/dcdsb.2015.20.153

[16]

Iasson Karafyllis, Lars Grüne. Feedback stabilization methods for the numerical solution of ordinary differential equations. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 283-317. doi: 10.3934/dcdsb.2011.16.283

[17]

Can Li, Weihua Deng, Lijing Zhao. Well-posedness and numerical algorithm for the tempered fractional differential equations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1989-2015. doi: 10.3934/dcdsb.2019026

[18]

Minoo Kamrani. Numerical solution of partial differential equations with stochastic Neumann boundary conditions. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5337-5354. doi: 10.3934/dcdsb.2019061

[19]

Yuri Bakhtin. Lyapunov exponents for stochastic differential equations with infinite memory and application to stochastic Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2006, 6 (4) : 697-709. doi: 10.3934/dcdsb.2006.6.697

[20]

M. Sumon Hossain, M. Monir Uddin. Iterative methods for solving large sparse Lyapunov equations and application to model reduction of index 1 differential-algebraic-equations. Numerical Algebra, Control & Optimization, 2019, 9 (2) : 173-186. doi: 10.3934/naco.2019013

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