Solving Stochastic Nonlinear Poisson-Boltzmann Equations Using a Collocation Method Based on RBFs
Mathematics, 2023 In this paper, we present a numerical scheme based on a collocation method to solve stochastic non-linear Poisson–Boltzmann equations (PBE). This equation is a generalized version of the non-linear Poisson–Boltzmann equations arising from a form of ...
Samaneh Mokhtari +4 more
doaj +1 more source
A bi-fidelity stochastic collocation method for transport equations with diffusive scaling and multi-dimensional random inputs [PDF]
Journal of Computational Physics, 2021 In this paper, we consider the development of efficient numerical methods for linear transport equations with random parameters and under the diffusive scaling. We extend to the present case the bi-fidelity stochastic collocation method introduced in [33,
Liu Liu, L. Pareschi, Xueyu Zhu
semanticscholar +1 more source
Multi-quadric collocation model of horizontal crustal movement [PDF]
Solid Earth, 2016 To establish the horizontal crustal movement velocity field of the Chinese mainland, a Hardy multi-quadric fitting model and collocation are usually used.
G. Chen, A. Zeng, F. Ming, Y. Jing
doaj +1 more source
Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties [PDF]
Networks Heterog. Media, 2021 Uncertainty in data is certainly one of the main problems in epidemiology, as shown by the recent COVID-19 pandemic. The need for efficient methods capable of quantifying uncertainty in the mathematical model is essential in order to produce realistic ...
Giulia Bertaglia +3 more
semanticscholar +1 more source
Error estimation and adaptivity for stochastic collocation finite elements Part I: single-level approximation [PDF]
SIAM Journal on Scientific Computing, 2021 A general adaptive refinement strategy for solving linear elliptic partial differential equation with random data is proposed and analysed herein. The adaptive strategy extends the a posteriori error estimation framework introduced by Guignard and Nobile
A. Bespalov, D. Silvester, Feng Xu
semanticscholar +1 more source
Fully Legendre spectral collocation technique for stochastic heat equations
Open Physics, 2021 For the stochastic heat equation (SHE), a very accurate spectral method is considered. To solve the SHE, we suggest using a shifted Legendre Gauss–Lobatto collocation approach in combination with a shifted Legendre Gauss–Radau collocation technique.
Abdelkawy Mohamed A. +3 more
doaj +1 more source
Multi-Index Stochastic Collocation for random PDEs [PDF]
Computer Methods in Applied Mechanics and Engineering, 2016 In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data.
AL HajiAli +3 more
openaire +3 more sources
Positive Stochastic Collocation for the Collocated Local Volatility Model
, 2021 This paper presents how to apply the stochastic collocation technique to assets that can not move below a boundary. It shows that the polynomial collocation towards a lognormal distribution does not work well. Then, the potentials issues of the related collocated local volatility model (CLV) are explored. Finally, a simple analytical expression for the
Floc'h, Fabien Le +1 more
openaire +2 more sources
On solving stochastic collocation systems with algebraic multigrid [PDF]
IMA Journal of Numerical Analysis, 2010 Stochastic collocation methods facilitate the numerical solution of partial differential equations (PDEs) with random data and give rise to long sequences of similar linear systems. When elliptic PDEs with random diffusion coefficients are discretized with mixed finite element methods in the physical domain we obtain saddle point systems.
Gordon, Andrew, Powell, Catherine
openaire +4 more sources
A Multilevel Stochastic Collocation Method for Schrödinger Equations with a Random Potential
SIAM/ASA J. Uncertain. Quantification, 2022 We propose and analyze a numerical method for time-dependent linear Schrödinger equations with 5 uncertain parameters in both the potential and the initial data.
T. Jahnke, B. Stein
semanticscholar +1 more source