[图书][B] Kernel-based approximation methods using Matlab

GE Fasshauer, MJ McCourt - 2015 - books.google.com
In an attempt to introduce application scientists and graduate students to the exciting topic of
positive definite kernels and radial basis functions, this book presents modern theoretical …

Bayesian probabilistic numerical methods

J Cockayne, CJ Oates, TJ Sullivan, M Girolami - SIAM review, 2019 - SIAM
Over forty years ago average-case error was proposed in the applied mathematics literature
as an alternative criterion with which to assess numerical methods. In contrast to worst-case …

Numerical solution of two-dimensional stochastic time-fractional Sine–Gordon equation on non-rectangular domains using finite difference and meshfree methods

F Mirzaee, S Rezaei, N Samadyar - Engineering Analysis with Boundary …, 2021 - Elsevier
Abstract The nonlinear Sine-Gordon equation is one of the widely used partial differential
equations that appears in various sciences and engineering. The main purpose of writing …

Probabilistic integration

FX Briol, CJ Oates, M Girolami, MA Osborne… - Statistical Science, 2019 - JSTOR
A research frontier has emerged in scientific computation, wherein discretisation error is
regarded as a source of epistemic uncertainty that can be modelled. This raises several …

Solution of time‐fractional stochastic nonlinear sine‐Gordon equation via finite difference and meshfree techniques

F Mirzaee, S Rezaei… - Mathematical Methods in …, 2022 - Wiley Online Library
In this article, we introduce a numerical procedure to solve time‐fractional stochastic sine‐
Gordon equation. The suggested technique is based on finite difference method and radial …

Combination of finite difference method and meshless method based on radial basis functions to solve fractional stochastic advection–diffusion equations

F Mirzaee, N Samadyar - Engineering with computers, 2020 - Springer
The present article develops a semi-discrete numerical scheme to solve the time-fractional
stochastic advection–diffusion equations. This method, which is based on finite difference …

Error analysis of kernel/GP methods for nonlinear and parametric PDEs

P Batlle, Y Chen, B Hosseini, H Owhadi… - Journal of Computational …, 2024 - Elsevier
We introduce a priori Sobolev-space error estimates for the solution of arbitrary nonlinear,
and possibly parametric, PDEs that are defined in the strong sense, using Gaussian process …

[HTML][HTML] Lévy noise versus Gaussian-noise-induced transitions in the Ghil–Sellers energy balance model

V Lucarini, L Serdukova… - Nonlinear Processes in …, 2022 - npg.copernicus.org
We study the impact of applying stochastic forcing to the Ghil–Sellers energy balance
climate model in the form of a fluctuating solar irradiance. Through numerical simulations …

[HTML][HTML] A shooting reproducing kernel Hilbert space method for multiple solutions of nonlinear boundary value problems

S Abbasbandy, B Azarnavid, MS Alhuthali - Journal of Computational and …, 2015 - Elsevier
In this work an iterative method is proposed to predict and demonstrate the existence and
multiplicity of solutions for nonlinear boundary value problems. In addition, the proposed …

Probabilistic numerical methods for PDE-constrained Bayesian inverse problems

J Cockayne, C Oates, T Sullivan… - AIP Conference …, 2017 - pubs.aip.org
This paper develops meshless methods for probabilistically describing discretisation error in
the numerical solution of partial differential equations. This construction enables the solution …