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Computing the density function of complex models with randomness by using polynomial expansions and the RVT technique. Application to the SIR epidemic model
12 references·0 citing·30 second hop
Computing the density function of complex models with randomness by using polynomial expansions and the RVT technique. Application to the SIR epidemic model (2020)Computing the density function of complex…Uncertainty quantification for random parabolic equations with nonhomogeneous boundary conditions on a bounded domain via the approximation of the probability density function (2018)Uncertainty quantification fo…Computational uncertainty quantification for random time‐discrete epidemiological models using adaptive gPC (2018)Computational uncertainty qua…Improving adaptive generalized polynomial chaos method to solve nonlinear random differential equations by the random variable transformation technique (2017)Improving adaptive generalize…Constructing adaptive generalized polynomial chaos method to measure the uncertainty in continuous models: A computational approach (2014)Constructing adaptive general…Error analysis of generalized polynomial chaos for nonlinear random ordinary differential equations (2012)Error analysis of generalized…On the convergence of generalized polynomial chaos expansions (2011)On the convergence of general…Spectral methods for uncertainty quantification : with applications to computational fluid dynamics (2010)Spectral methods for uncertai…Galerkin Method for Wave Equations with Uncertain Coefficients (2008)Galerkin Method for Wave Equa…Convergence properties of polynomial chaos approximations for L2 random variables. (2007)Convergence properties of pol…The approximate solutions of some stochastic differential equations using transformations (2004)The approximate solutions of …The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)Generalized polynomial chaos for nonlinear random delay differential equations (2017)Combining Polynomial Chaos Expansions and the Random Variable Transformation Technique to Approximate the Density Function of Stochastic Problems, Including Some Epidemiological Models (2019)Improving the Approximation of the First- and Second-Order Statistics of the Response Stochastic Process to the Random Legendre Differential Equation (2019)Application of Wiener-Hermite Expansion to Nonstationary Random Vibration of a Duffing Oscillator (1983)A proposed technique of SFEM on solving ordinary random differential equation (2004)Uncertainty quantification analysis of the biological Gompertz model subject to random fluctuations in all its parameters (2020)High-Order Collocation Methods for Differential Equations with Random Inputs (2005)Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs (2011)Adaptive Smolyak Pseudospectral Approximations (2013)Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark (2021)On the accuracy of the polynomial chaos approximation (2004)Efficient and Robust Uncertainty Quantification in Reservoir Simulation with Polynomial Chaos Expansions and Non-intrusive Spectral Projection (2011)On the convergence of the stochastic Galerkin method for random elliptic partial differential equations (2013)Efficient uncertainty quantification in fully-integrated surface and subsurface hydrologic simulations (2017)Numerical Methods for Stochastic Computations: A Spectral Method Approach (2010)On the convergence of adaptive gPC for non-linear random difference equations: Theoretical analysis and some practical recommendations (2018)Stochastic Differential Equations (2003)Stochastic Partial Differential Equations (2009)An Introduction to Computational Stochastic PDEs (2014)Second order linear differential equations with analytic uncertainties: Stochastic analysis via the computation of the probability density function (2020)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)Simulation-based optimal Bayesian experimental design for nonlinear systems (2012)Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies (2014)Stochastic finite element methods for partial differential equations with random input data (2014)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network (2007)A stochastic collocation method for the second order wave equation with a discontinuous random speed (2012)Robust Uncertainty Propagation in Systems of Conservation Laws with the Entropy Closure Method (2013)
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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2010Spectral methods for uncertainty quantification : with applications to computational fluid dynamics572 cited
  • 2011On the convergence of generalized polynomial chaos expansions414 cited
  • 2008Galerkin Method for Wave Equations with Uncertain Coefficients112 cited
  • 2004The approximate solutions of some stochastic differential equations using transformations44 cited
  • 2007Convergence properties of polynomial chaos approximations for L2 random variables.28 cited
  • 2012Error analysis of generalized polynomial chaos for nonlinear random ordinary differential equations21 cited
  • 2018Uncertainty quantification for random parabolic equations with nonhomogeneous boundary conditions on a bounded domain via the approximation of the probability density function18 cited
  • 2017Improving adaptive generalized polynomial chaos method to solve nonlinear random differential equations by the random variable transformation technique17 cited
  • 2018Computational uncertainty quantification for random time‐discrete epidemiological models using adaptive gPC16 cited
  • 2014Constructing adaptive generalized polynomial chaos method to measure the uncertainty in continuous models: A computational approach14 cited

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