Generalized polynomial chaos for nonlinear random delay differential equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2016.12.004 ◽

2017 ◽

Vol 115 ◽

pp. 16-31 ◽

Author(s):

Wenjie Shi ◽

Chengjian Zhang

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Polynomial Chaos ◽

Random Delay ◽

Generalized Polynomial Chaos ◽

Generalized Polynomial ◽

Delay Differential

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RANDOM DELAY DIFFERENTIAL EQUATIONS AND INVERSE PROBLEMS FOR AGGREGATE DATA PROBLEMS

Eurasian Journal of Mathematical and Computer Applications ◽

10.32523/2306-6172-2018-6-4-4-16 ◽

2018 ◽

Vol 6 (4) ◽

pp. 4-16

Author(s):

H.T. Banks ◽

◽

W.C. Thompson

Keyword(s):

Inverse Problems ◽

Differential Equations ◽

Delay Differential Equations ◽

Aggregate Data ◽

Random Delay ◽

Delay Differential

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Principal Floquet subspaces and exponential separations of type Ⅱ with applications to random delay differential equations

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2018265 ◽

2018 ◽

Vol 38 (12) ◽

pp. 6163-6193

Author(s):

Janusz Mierczyński ◽

◽

Sylvia Novo ◽

Rafael Obaya ◽

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Random Delay ◽

Delay Differential

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Error analysis of generalized polynomial chaos for nonlinear random ordinary differential equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2012.08.007 ◽

2012 ◽

Vol 62 (12) ◽

pp. 1954-1964 ◽

Author(s):

Wenjie Shi ◽

Chengjian Zhang

Keyword(s):

Differential Equations ◽

Error Analysis ◽

Ordinary Differential Equations ◽

Polynomial Chaos ◽

Generalized Polynomial Chaos ◽

Generalized Polynomial

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Polynomial Chaos Expansions for the Stability Analysis of Uncertain Delay Differential Equations

SIAM/ASA Journal on Uncertainty Quantification ◽

10.1137/15m1029618 ◽

2017 ◽

Vol 5 (1) ◽

pp. 278-303 ◽

Author(s):

Rossana Vermiglio

Keyword(s):

Stability Analysis ◽

Differential Equations ◽

Delay Differential Equations ◽

Polynomial Chaos ◽

The Stability ◽

Polynomial Chaos Expansions ◽

Delay Differential

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Mean-square random attractors of stochastic delay differential equations with random delay

Discrete & Continuous Dynamical Systems - B ◽

10.3934/dcdsb.2013.18.1715 ◽

2013 ◽

Vol 18 (6) ◽

pp. 1715-1734 ◽

Author(s):

Fuke Wu ◽

◽

Peter E. Kloeden ◽

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Mean Square ◽

Stochastic Delay Differential Equations ◽

Random Delay ◽

Stochastic Delay ◽

Random Attractors ◽

Delay Differential

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Analyticity, Regularity, and Generalized Polynomial Chaos Approximation of Stochastic, Parametric Parabolic Two-Scale Partial Differential Equations

Acta Mathematica Vietnamica ◽

10.1007/s40306-019-00345-2 ◽

2019 ◽

Vol 45 (1) ◽

pp. 217-247

Author(s):

Viet Ha Hoang

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Polynomial Chaos ◽

Generalized Polynomial Chaos ◽

Partial Differential ◽

Generalized Polynomial

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Improving adaptive generalized polynomial chaos method to solve nonlinear random differential equations by the random variable transformation technique

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2017.02.011 ◽

2017 ◽

Vol 50 ◽

pp. 1-15 ◽

Author(s):

J.-C. Cortés ◽

J.-V. Romero ◽

M.-D. Roselló ◽

R.-J. Villanueva

Keyword(s):

Differential Equations ◽

Polynomial Chaos ◽

Random Variable ◽

Generalized Polynomial Chaos ◽

Transformation Technique ◽

Variable Transformation ◽

Generalized Polynomial ◽

Random Differential Equations

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An adaptive multi-element generalized polynomial chaos method for stochastic differential equations

Journal of Computational Physics ◽

10.1016/j.jcp.2005.03.023 ◽

2005 ◽

Vol 209 (2) ◽

pp. 617-642 ◽

Author(s):

Xiaoliang Wan ◽

George Em Karniadakis

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Polynomial Chaos ◽

Generalized Polynomial Chaos ◽

Generalized Polynomial

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Polynomial Chaos and Its Application to Delay Differential Equations with Uncertainties

Mathematics in Industry - Progress in Industrial Mathematics at ECMI 2010 ◽

10.1007/978-3-642-25100-9_33 ◽

2012 ◽

pp. 283-289

Author(s):

Manuel Villegas Caballero

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Polynomial Chaos ◽

Delay Differential

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Do the generalized polynomial chaos and Fröbenius methods retain the statistical moments of random differential equations?

Applied Mathematics Letters ◽

10.1016/j.aml.2012.12.013 ◽

2013 ◽

Vol 26 (5) ◽

pp. 553-558 ◽

Author(s):

Benito M. Chen-Charpentier ◽

J.-C. Cortés ◽

J.-V. Romero ◽

M.-D. Roselló

Keyword(s):

Differential Equations ◽

Polynomial Chaos ◽

Statistical Moments ◽

Generalized Polynomial Chaos ◽

Generalized Polynomial ◽

Random Differential Equations

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