Diffusion probabilistic models (DPMs) have exhibited excellent performance for high-fidelity
image generation while suffering from inefficient sampling. Recent works accelerate the …

In this paper we consider the construction, analysis, implementation and application of
exponential integrators. The focus will be on two types of stiff problems. The first one is …

Exponential Euler discrete schemes have been widely employed in the studies of Caputo
fractional order differential equations, but almost no literature concerns the Caputo–Fabrizio …

It is challenging to numerically solve oscillatory Hamiltonian systems due to the stiffness of
the problems and the requirement of highly stable and energy-preserving schemes. The …

We rigorously study a novel type of trigonometric Fourier collocation methods for solving
multi-frequency oscillatory second-order ordinary differential equations (ODEs) q^ ′ ′ (t)+ …

In text-to-speech (TTS) synthesis, diffusion models have achieved promising generation
quality. However, because of the pre-defined data-to-noise diffusion process, their prior …

We formulate probabilistic numerical approximations to solutions of ordinary differential
equations (ODEs) as problems in Gaussian process (GP) regression with nonlinear …

In the present work, a kind of trigonometric collocation methods based on Lagrange basis
polynomials is developed for effectively solving multi-frequency oscillatory second-order …

Many important applications are modelled by differential equations with positive solutions.
However, it remains an outstanding open problem to develop numerical methods that are …

This paper reviews the key building blocks needed to develop a mechanistic model for use
as an operational production tool. The Chinese Hamster Ovary (CHO) cell, one of the most …