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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

This paper develops meshless methods for probabilistically describing discretisation error in
the numerical solution of partial differential equations. This construction enables the solution …