Legendre Approximation-Based Stability Test for Distributed Delay Systems: Legendre approximation-based stability test for distributed delay systems

Authors: Alejandro Castaño, Mathieu Bajodek, Sabine Mondié

Source: SIAM Journal on Numerical Analysis. 63:641-660

Subject Terms: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), Stability theory of functional-differential equations, necessary and sufficient stability condition, linear functional differential equation, Sensitivity, stability, well-posedness, Numerical approximation of solutions of functional-differential equations, Legendre polynomials approximation

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Computational methods of solving the boundary value problems for the loaded differential and Fredholm integro‐differential equations: Computational methods of solving the boundary value problems for the loaded differential and Fredholm integro-differential equations

Authors: Dulat Dzhumabaev

Source: Mathematical Methods in the Applied Sciences. 41:1439-1462

Subject Terms: Integro-ordinary differential equations, solvability criteria, algorithm, Fredholm integro-differential equation, Fredholm integral equations, 0101 mathematics, Numerical approximation of solutions of functional-differential equations, 01 natural sciences, \(\delta_m (\theta)\) general solution

File Description: application/xml

Access URL: https://onlinelibrary.wiley.com/doi/full/10.1002/mma.4674
https://ui.adsabs.harvard.edu/abs/2018MMAS...41.1439D/abstract

A BRIEF SURVEY ON THE NUMERICAL DYNAMICS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS: A brief survey on the numerical dynamics for functional differential equations

Authors: Barnabas M. Garay

Source: International Journal of Bifurcation and Chaos. 15:729-742

Subject Terms: invariant manifolds, hyperbolic periodic orbits, Attractors and repellers of smooth dynamical systems and their topological structure, saddle structure, Kamke monotonicity, Generic properties, structural stability of dynamical systems, Numerical methods for Hamiltonian systems including symplectic integrators, Numerical approximation of solutions of functional-differential equations, Stability theory for smooth dynamical systems, 01 natural sciences, Runge-Kutta discretizations, survey paper, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, compact attractors, hyperbolic equilibria, retarded functional differential equations, error estimates, Research exposition (monographs, survey articles) pertaining to numerical analysis, structural stability, Periodic orbits of vector fields and flows, inertial manifolds, delay equations, center-unstable manifolds, 0101 mathematics, Error bounds for numerical methods for ordinary differential equations

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Access URL: http://www.math.bme.hu/~garay/gfarkas.pdf
https://ui.adsabs.harvard.edu/abs/2006mcds.book...33G/abstract
https://ui.adsabs.harvard.edu/abs/2005IJBC...15..729G/abstract
http://www.math.bme.hu/~garay/gfarkas.pdf
https://www.worldscientific.com/doi/abs/10.1142/S021812740501251X
https://dblp.uni-trier.de/db/journals/ijbc/ijbc15.html#Garay05

Weak approximation of stochastic differential delay equations

Authors: Buckwar, Evelyn, Shardlow, Tony

Source: IMA Journal of Numerical Analysis. 25:57-86

Subject Terms: Numerical solutions to stochastic differential and integral equations, ddc:330, 330 Wirtschaft, Stochastic functional-differential equations, discrete time approximation, Stochastic delay equations, Theoretical approximation of solutions, Stochastic partial differential equations, Stochastic delay equations,Theoretical approximation of solutions,Stochastic partial differential equations,Stability and convergence of numerical approximations, Numerical approximation of solutions of functional-differential equations, 01 natural sciences, Stochastic ordinary differential equations (aspects of stochastic analysis), stochastic differential equations with time delay, forward Euler approximation, Stability and convergence of numerical approximations, weak convergence, 0101 mathematics, Computational methods for stochastic equations (aspects of stochastic analysis), Monte Carlo simulation

File Description: application/xml; application/pdf

Access URL: https://edoc.hu-berlin.de/bitstream/18452/4297/1/88.pdf
https://researchportal.bath.ac.uk/en/publications/weak-approximation-of-stochastic-differential-delay-equations
https://academic.oup.com/imajna/article-abstract/25/1/57/731462
https://edoc.hu-berlin.de/bitstream/18452/4297/1/88.pdf
https://academic.oup.com/imajna/article-abstract/25/1/57/731462/Weak-approximation-of-stochastic-differential
https://edoc.hu-berlin.de/handle/18452/4297
http://hdl.handle.net/10419/62718
http://edoc.hu-berlin.de/18452/4297
https://doi.org/10.18452/3645
https://www.econstor.eu/bitstream/10419/62718/1/725952385.pdf

Retarded differential equations

Authors: Christopher T. H. Baker

Source: Numerical Analysis: Historical Developments in the 20th Century ISBN: 9780444506177

Subject Terms: retarded differential equations, convergence, Numerics, Applied Mathematics, Numerical stability, Numerical approximation of solutions of functional-differential equations, Numerical methods for initial value problems involving ordinary differential equations, 01 natural sciences, Mesh and densely defined approximations, Computational Mathematics, Order of convergence, Delay and neutral delay differential equations, Retarded differential equations, Continuity and stability, 0101 mathematics, Convergence

File Description: application/xml

Access URL: https://zbmath.org/1566020
https://doi.org/10.1016/s0377-0427(00)00476-3
https://www.sciencedirect.com/science/article/pii/S0377042700004763
http://www.sciencedirect.com/science/article/pii/S0377042700004763
https://www.sciencedirect.com/science/article/abs/pii/S0377042700004763
http://ui.adsabs.harvard.edu/abs/2000JCoAM.125..309B/abstract
https://dialnet.unirioja.es/servlet/articulo?codigo=700247

Exponential Collocation Method for Solutions of Singularly Perturbed Delay Differential Equations: Exponential collocation method for solutions of singularly perturbed delay differential equations

Authors: Yüzbaşı, Şuayip, Sezer, Mehmet

Source: Abstract and Applied Analysis, Vol 2013 (2013)
Abstr. Appl. Anal.

Subject Terms: 0209 industrial biotechnology, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, QA1-939, Numerical methods for functional-differential equations, 02 engineering and technology, 0101 mathematics, Numerical approximation of solutions of functional-differential equations, 01 natural sciences, Mathematics, Numerical solution of singularly perturbed problems involving ordinary differential equations, Theoretical approximation of solutions to ordinary differential equations

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https://doi.org/10.1155/2013/493204
https://doaj.org/article/2ae546a7399644f99d2bee6a7fcf043a
https://projecteuclid.org/download/pdfview_1/euclid.aaa/1393512015
https://downloads.hindawi.com/journals/aaa/2013/493204.pdf
https://doaj.org/article/2ae546a7399644f99d2bee6a7fcf043a
http://downloads.hindawi.com/journals/aaa/2013/493204.pdf
https://cyberleninka.org/article/n/514434.pdf
https://www.hindawi.com/journals/aaa/2013/493204/
http://projecteuclid.org/euclid.aaa/1393512015

Direct operatorial tau method for pantograph-type equations

Authors: Damian Trif

Source: Applied Mathematics and Computation. 219:2194-2203

Subject Terms: pantograph equations, tau method, Linear functional-differential equations, Software, source code, etc. for problems pertaining to ordinary differential equations, Chebyshev polynomials, 0101 mathematics, Numerical approximation of solutions of functional-differential equations, 01 natural sciences

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/S0096300312008582
https://dblp.uni-trier.de/db/journals/amc/amc219.html#Trif12

Numerical stability of higher-order derivative methods for the pantograph equation

Authors: Wanjin Lv, Hui Li

Source: Applied Mathematics and Computation. 218:5739-5745

Subject Terms: pantograph equations, numerical example, delay differential equations, numerical stability, variable stepsize, infinite lag, Mesh generation, refinement, and adaptive methods for ordinary differential equations, Numerical methods for functional-differential equations, higher-order derivative method, 0101 mathematics, Numerical approximation of solutions of functional-differential equations, Stability and convergence of numerical methods for ordinary differential equations, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/6045333
https://doi.org/10.1016/j.amc.2011.11.071
http://www.sciencedirect.com/science/article/pii/S0096300311014147
https://doi.org/10.1016/j.amc.2011.11.071
https://dblp.uni-trier.de/db/journals/amc/amc218.html#LvL12a
https://www.sciencedirect.com/science/article/pii/S0096300311014147

Covariant transformations of basis differential-difference schemes in a plane

Authors: V. A. Korobitsyn

Source: Computational Mathematics and Mathematical Physics. 51:1915-1922

Subject Terms: Finite difference and finite volume methods for ordinary differential equations, Cartesian coordinate system, differential-difference schemes, basis operator method, consistent difference approximations, 0103 physical sciences, Numerical methods for functional-differential equations, 0101 mathematics, Numerical approximation of solutions of functional-differential equations, 01 natural sciences, Hybrid systems of functional-differential equations

File Description: application/xml

Access URL: https://zbmath.org/6057630
https://doi.org/10.1134/s0965542511110121
https://ui.adsabs.harvard.edu/abs/2011CMMPh..51.1915K/abstract
https://link.springer.com/article/10.1134/S0965542511110121

A multi-interval Chebyshev collocation approach for the stability of periodic delay systems with discontinuities

Authors: Firas A. Khasawneh, Eric A. Butcher, Brian P. Mann

Source: Communications in Nonlinear Science and Numerical Simulation. 16:4408-4421

Subject Terms: numerical examples, periodic delay systems, 0209 industrial biotechnology, convergence, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, Numerical methods for functional-differential equations, spectral method, 02 engineering and technology, stability, multi-interval Chebyshev collocation, Numerical approximation of solutions of functional-differential equations, Numerical methods for initial value problems involving ordinary differential equations, 01 natural sciences, Periodic solutions to functional-differential equations, Linear functional-differential equations, 0103 physical sciences, Stability and convergence of numerical methods for ordinary differential equations

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Access URL: https://zbmath.org/5941884
https://doi.org/10.1016/j.cnsns.2011.03.025
http://ui.adsabs.harvard.edu/abs/2011CNSNS..16.4408K/abstract
https://arizona.pure.elsevier.com/en/publications/a-multi-interval-chebyshev-collocation-approach-for-the-stability
http://www.sciencedirect.com/science/article/pii/S1007570411001559
https://www.sciencedirect.com/science/article/pii/S1007570411001559

Domain-decomposition method for the global dynamics of delay differential equations with unimodal feedback

Authors: Gergely Röst, Jianhong Wu

Source: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 463:2655-2669

Subject Terms: Asymptotic theory of functional-differential equations, Qualitative investigation and simulation of models involving functional-differential equations, QA Mathematics / matematika, heteroclinic orbits, 0103 physical sciences, delay-induced chaos, stability, 0101 mathematics, Numerical approximation of solutions of functional-differential equations, global attractivity, 01 natural sciences

File Description: application/xml; application/pdf

Access URL: https://royalsocietypublishing.org/doi/10.1098/rspa.2007.1890
https://rspa.royalsocietypublishing.org/content/463/2086/2655
http://rspa.royalsocietypublishing.org/content/royprsa/463/2086/2655.full.pdf
http://core.ac.uk/display/11856008
http://real.mtak.hu/3831/
https://ui.adsabs.harvard.edu/abs/2007RSPSA.463.2655R/abstract

A Taylor polynomial approach for solving differential-difference equations

Authors: Gülsu, Mustafa, Sezer, Mehmet

Contributors: MÜ,Fen Fakültesi, Matematik Bölümü, Gülsu, Mustafa

Source: Journal of Computational and Applied Mathematics. 186:349-364

Subject Terms: Taylor polynomial solutions, Computational Mathematics, Taylor polynomials and series, Applied Mathematics, differential-difference equations, Taylor matrix method, 0101 mathematics, Numerical approximation of solutions of functional-differential equations, Numerical methods for initial value problems involving ordinary differential equations, 01 natural sciences, Differential-difference equations

File Description: application/xml; application/pdf

Access URL: https://zbmath.org/2231265
https://doi.org/10.1016/j.cam.2005.02.009
https://www.sciencedirect.com/science/article/pii/S0377042705000993
https://core.ac.uk/display/82367225
http://acikerisim.mu.edu.tr/xmlui/handle/20.500.12809/5213
https://www.sciencedirect.com/science/article/abs/pii/S0377042705000993
http://ui.adsabs.harvard.edu/abs/2006JCoAM.186..349G/abstract
https://dl.acm.org/doi/10.5555/1124435.1716935
https://hdl.handle.net/20.500.12809/5213
https://doi.org/10.1016/j.cam.2005.02.009

Open issues in devising software for the numerical solution of implicit delay differential equations

Authors: GUGLIELMI, NICOLA

Source: Journal of Computational and Applied Mathematics. 185:261-277

Subject Terms: RADAR5, pantograph equation, numerical examples, Applied Mathematics, Numerical code, 3-stage Radau IIA Runge-Kutta method, RADAR5, Implicit delay differential equations, Radau method, Numerical code, Error control, Numerical approximation of solutions of functional-differential equations, Error control, Numerical methods for initial value problems involving ordinary differential equations, 01 natural sciences, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Computational Mathematics, Radau method, 0101 mathematics, Implicit delay differential equations, Error bounds for numerical methods for ordinary differential equations

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Access URL: https://www.sciencedirect.com/science/article/abs/pii/S0377042705001147
https://ui.adsabs.harvard.edu/abs/2006JCoAM.185..261G/abstract
https://www.sciencedirect.com/science/article/pii/S0377042705001147
https://dialnet.unirioja.es/servlet/articulo?codigo=1276509
https://univaq.it/~guglielm/PAPERS/DDESoft.pdf
https://core.ac.uk/display/82776617

Identification of the initial function for discretized delay differential equations

Authors: Baker, Christopher T. H., Parmuzin, Evgeny I.

Contributors: University College Chester, Institute of Numerical Mathematics, Russian Academy of Sciences

Source: Baker, C T H & Parmuzin, E I 2005, 'Identification of the initial function for discretized delay differential equations', Journal of Computational and Applied Mathematics, vol. 181, no. 2, pp. 420-441. https://doi.org/10.1016/j.cam.2004.11.035

Subject Terms: convergence, Discrete adjoint equations, Identification problem, Applied Mathematics, regularization parameter, Numerical approximation of solutions of functional-differential equations, Discrete delay differential equations, 01 natural sciences, discrete adjoint equations, Discrete fundamental matrices, Computational Mathematics, Data assimilation, discrete delay differential equations, Initial function, Regularization parameter, discrete adjoint equation, initial function, Inverse problems for functional-differential equations, 0101 mathematics, Numerical solution of inverse problems involving ordinary differential equations, identification problem, data assimilation, discrete delay differential equation

File Description: application/xml

Access URL: https://research.manchester.ac.uk/en/publications/6839ce44-d9ef-40cb-acb0-da532ab435aa
https://doi.org/10.1016/j.cam.2004.11.035
http://ui.adsabs.harvard.edu/abs/2005JCoAM.181..420B/abstract
https://www.sciencedirect.com/science/article/pii/S0377042704005941
http://www.escholar.manchester.ac.uk/uk-ac-man-scw:206734
https://www.sciencedirect.com/science/article/abs/pii/S0377042704005941
http://www.chester.ac.uk/sites/files/chester/Identification%20of%20the%20Initial%20Function%20for%20Discretized%20Delay%20Differential%20Equations.pdf
https://chesterrep.openrepository.com/handle/10034/67639

Stability of the Rosenbrock methods for the neutral delay differential-algebraic equations

Authors: S. Y. Dong, Yan Xu, Jingjun Zhao, Ming Liu

Source: Applied Mathematics and Computation. 168:1128-1144

Subject Terms: Numerical methods for differential-algebraic equations, Rosenbrock methods, stability, Numerical approximation of solutions of functional-differential equations, Numerical methods for initial value problems involving ordinary differential equations, 01 natural sciences, Neutral functional-differential equations, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, numerical example, neutral delay differential algebraic equations, Runge-Kutta method, 0101 mathematics, Stability and convergence of numerical methods for ordinary differential equations, Implicit ordinary differential equations, differential-algebraic equations

File Description: application/xml

Access URL: https://dblp.uni-trier.de/db/journals/amc/amc168.html#ZhaoXDL05
https://www.sciencedirect.com/science/article/abs/pii/S009630030400668X

A Newton-Picard Collocation Method for Periodic Solutions of Delay Differential Equations: A Newton-Picard collocation method for periodic solutions of delay differential equations

Authors: Kurt Lust, Koen Verheyden

Source: BIT Numerical Mathematics. 45:605-625

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, collocation, numerical examples, STABILITY, autonomous delay differential equations, numerical bifurcation analysis, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, linearized periodic boundary value problem, BIFURCATION-ANALYSIS, periodic solution, periodic solutions, Newton-Picard, COMPUTATION, Numerical approximation of solutions of functional-differential equations, 01 natural sciences, Periodic solutions to functional-differential equations, collocation method, Floquet multipliers, delay differential equation, Newton-Picard method, 0101 mathematics

File Description: application/xml

Access URL: http://www.cs.kuleuven.be/publicaties/rapporten/tw/TW357.pdf
https://zbmath.org/2246779
https://doi.org/10.1007/s10543-005-0013-4
https://hdl.handle.net/11370/f7ddc912-a003-4535-a306-f3a2c76d9680
https://research.rug.nl/en/publications/f7ddc912-a003-4535-a306-f3a2c76d9680
https://doi.org/10.1007/s10543-005-0013-4
https://www.rug.nl/research/portal/files/2931390/2005BITNumMathVerheyden.pdf
https://research.rug.nl/en/publications/a-newton-picard-collocation-method-for-periodic-solutions-of-dela
https://pure.rug.nl/ws/files/2931390/2005BITNumMathVerheyden.pdf
https://www.narcis.nl/publication/RecordID/oai%3Apure.rug.nl%3Apublications%2Ff7ddc912-a003-4535-a306-f3a2c76d9680
https://link.springer.com/article/10.1007%2Fs10543-005-0013-4
https://link.springer.com/content/pdf/10.1007/s10543-005-0013-4.pdf

Effective approaches to explore rich dynamics of delay-differential equations

Authors: Mingshu Peng

Source: Chaos, Solitons & Fractals. 25:1131-1140

Subject Terms: 0301 basic medicine, 03 medical and health sciences, bifurcation, 0103 physical sciences, delay differential equation, discretization, Numerical approximation of solutions of functional-differential equations, 01 natural sciences, Bifurcation theory of functional-differential equations, Periodic solutions to functional-differential equations

File Description: application/xml

Access URL: https://zbmath.org/2191094
https://doi.org/10.1016/j.chaos.2004.11.086
https://ideas.repec.org/a/eee/chsofr/v25y2005i5p1131-1140.html
https://ui.adsabs.harvard.edu/abs/2005CSF....25.1131P/abstract
https://www.sciencedirect.com/science/article/abs/pii/S0960077905000093

Global robust exponential stability analysis for interval neural networks with time-varying delays

Authors: Xiaofeng Liao, Rong Zhang, Ashutosh Prasad, Chuandong Li

Source: Chaos, Solitons & Fractals. 25:751-757

Subject Terms: 0202 electrical engineering, electronic engineering, information engineering, 02 engineering and technology, Numerical approximation of solutions of functional-differential equations, Stability and convergence of numerical methods for ordinary differential equations

File Description: application/xml

Access URL: http://ui.adsabs.harvard.edu/abs/2005CSF....25..751L/abstract
https://ideas.repec.org/a/eee/chsofr/v25y2005i3p751-757.html
https://www.sciencedirect.com/science/article/pii/S0960077904007787

RUNGE–KUTTA METHODS FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS: Runge-Kutta methods for retarded functional differential equations

Authors: MASET, STEFANO, TORELLI, LUCIO, R. VERMIGLIO

Contributors: Maset, Stefano, Torelli, Lucio, R., Vermiglio

Source: Mathematical Models and Methods in Applied Sciences. 15:1203-1251

Subject Terms: Retarded Functional Differential Equations, Runge-Kutta methods, Explicit Methods, Order conditions, order conditions, Numerical approximation of solutions of functional-differential equations, Runge–Kutta method, Numerical methods for initial value problems involving ordinary differential equations, 01 natural sciences, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, retarded functional differential equations, explicit method, Retarded functional differential equation, Retarded functional differential equations, Runge–Kutta methods, explicit methods, initial value problems, 0101 mathematics, continuous Runge-Kutta methods

File Description: application/xml; STAMPA; application/pdf

Access URL: https://zbmath.org/2220073
https://doi.org/10.1142/s0218202505000716
http://hdl.handle.net/11368/1697476
https://www.worldscientific.com/doi/abs/10.1142/S0218202505000716
https://dialnet.unirioja.es/servlet/articulo?codigo=1258160
https://hdl.handle.net/11368/1697476

Analysis of Newton’s Method to Compute Travelling Waves in Discrete Media: Analysis of Newton's method to compute travelling waves in discrete media

Authors: S. M. Verduyn Lunel, Hermen Jan Hupkes

Source: Journal of Dynamics and Differential Equations. 17:523-572

Subject Terms: functional differential equations, Newton's method, Computation of travelling waves, numerical computation, Ising model, 0103 physical sciences, General theory of functional-differential equations, discrete media, 0101 mathematics, Numerical approximation of solutions of functional-differential equations, bistable lattice differential equations, 01 natural sciences, myelinated nerve fibers

File Description: application/xml

Access URL: https://ui.adsabs.harvard.edu/abs/2005JDDE...17..523H/abstract
https://link.springer.com/article/10.1007/s10884-005-5809-z
http://pub.math.leidenuniv.nl/~hupkeshj/jdde2005.pdf
https://rd.springer.com/article/10.1007/s10884-005-5809-z