Xiao Qi
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Xiao Qi has a total of 13 co-authors. Here are the top co-authors by number of shared publications:
- Yubin Yan
School of Computer and Engineering Sciences, University of Chester, Chester, UK
5 shared publications Amiya K. Pani
1 shared publication- Chuanju Xu
School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen, China
1 shared publication - George Dewhirst
School of Computer and Engineering Sciences, University of Chester, Chester, UK
1 shared publication Lihua Wang
1 shared publication- Lihua Wang
College of Acupuncture and Orthopedics
1 shared publication
Latest Publications
- Open Access
- 14 September 2026
- Published by Elsevier in Journal of Computational and Applied Mathematics
- Vol. 493
Milstein convolution quadrature approximation to stochastic semilinear Volterra integro-differential equations
- 14 September 2026
- Published by Elsevier in Journal of Computational and Applied Mathematics
- Vol. 493
Open AccessMilstein convolution quadrature approximation to stochastic semilinear Volterra integro-differential equations
- Open Access
- 24 February 2026
- Published by Springer Nature in Journal of Scientific Computing
- Vol. 107 (1) , 10
An Efficient Tamed Milstein Scheme for the Stochastic Allen-Cahn Equation with Multiplicative Noise
This paper investigates the strong convergence of a fully discrete scheme for the stochastic Allen–Cahn equation with multiplicative noise, combining a tamed Milstein method for the temporal discretization with the finite element method in space. The proposed method is shown to be unconditionally stable in spatial dimensions $$d\in \{1,2,3\}$$ . Beyond the inherent challenges caused by, see, e.g., [1], the cubic non-globally Lipschitz drift term and multiplicative driving noise in the convergence analysis, the Milstein scheme further complicates the error estimation of the noise term compared to the Euler-Maruyama discretization. By introducing a novel auxiliary process, we rigorously establish strong convergence rates in both space and time under mild assumptions for $$d\in \{1,2\}$$ . Our analysis shows that the temporal convergence order is doubled compared to that of tamed Euler-Maruyama scheme. Numerical experiments are provided to confirm the theoretical results and to demonstrate that the proposed scheme exhibits improved robustness over the pure semi-implicit Milstein method.- 24 February 2026
- Published by Springer Nature in Journal of Scientific Computing
- Vol. 107 (1) , 10
Open AccessAn Efficient Tamed Milstein Scheme for the Stochastic Allen-Cahn Equation with Multiplicative Noise
This paper investigates the strong convergence of a fully discrete scheme for the stochastic Allen–Cahn equation with multiplicative noise, combining a tamed Milstein method for the temporal discretization with the finite element method in space. The proposed method is shown to be unconditionally stable in spatial dimensions $$d\in \{1,2,3\}$$ . Beyond the inherent challenges caused by, see, e.g., [1], the cubic non-globally Lipschitz drift term and multiplicative driving noise in the convergence analysis, the Milstein scheme further complicates the error estimation of the noise term compared to the Euler-Maruyama discretization. By introducing a novel auxiliary process, we rigorously establish strong convergence rates in both space and time under mild assumptions for $$d\in \{1,2\}$$ . Our analysis shows that the temporal convergence order is doubled compared to that of tamed Euler-Maruyama scheme. Numerical experiments are provided to confirm the theoretical results and to demonstrate that the proposed scheme exhibits improved robustness over the pure semi-implicit Milstein method. - Open Access
Drift-Randomized Milstein-Galerkin Finite Element Method for Semilinear Stochastic Evolution Equations
Kruse and Wu [Math. Comp. 88 (2019) 2793--2825] proposed a fully discrete randomized Galerkin finite element method for semilinear stochastic evolution equations (SEEs) driven by additive noise and showed that this method attains a temporal strong convergence rate exceeding order $\frac{1}{2}$ without imposing any differentiability assumptions on the drift nonlinearity. They further discussed a potential extension of the randomized method to SEEs with multiplicative noise and introduced the so-called drift-randomized Milstein-Galerkin finite element fully discrete scheme, but without providing a corresponding strong convergence analysis. This paper aims to fill this gap by rigorously analyzing the strong convergence behavior of the drift-randomized Milstein-Galerkin finite element scheme. By avoiding the use of differentiability assumptions on the nonlinear drift term, we establish strong convergence rates in both space and time for the proposed method. The obtained temporal convergence rate is $O(Δt^{1-\varepsilon_0})$, where $Δt$ denotes the time step size and $\varepsilon_0$ is an arbitrarily small positive number. Numerical experiments are reported to validate the theoretical findings.Open AccessDrift-Randomized Milstein-Galerkin Finite Element Method for Semilinear Stochastic Evolution Equations
Kruse and Wu [Math. Comp. 88 (2019) 2793--2825] proposed a fully discrete randomized Galerkin finite element method for semilinear stochastic evolution equations (SEEs) driven by additive noise and showed that this method attains a temporal strong convergence rate exceeding order $\frac{1}{2}$ without imposing any differentiability assumptions on the drift nonlinearity. They further discussed a potential extension of the randomized method to SEEs with multiplicative noise and introduced the so-called drift-randomized Milstein-Galerkin finite element fully discrete scheme, but without providing a corresponding strong convergence analysis. This paper aims to fill this gap by rigorously analyzing the strong convergence behavior of the drift-randomized Milstein-Galerkin finite element scheme. By avoiding the use of differentiability assumptions on the nonlinear drift term, we establish strong convergence rates in both space and time for the proposed method. The obtained temporal convergence rate is $O(Δt^{1-\varepsilon_0})$, where $Δt$ denotes the time step size and $\varepsilon_0$ is an arbitrarily small positive number. Numerical experiments are reported to validate the theoretical findings. - Open Access
- 28 January 2026
- Published by Elsevier in Applied Numerical Mathematics
- Vol. 224, 22-36
Long time stability and strong convergence of an efficient tamed scheme for stochastic Allen-Cahn equation driven by additive white noise
- 28 January 2026
- Published by Elsevier in Applied Numerical Mathematics
- Vol. 224, 22-36
Open AccessLong time stability and strong convergence of an efficient tamed scheme for stochastic Allen-Cahn equation driven by additive white noise
- Open Access
- 5 December 2025
- Published by Elsevier in Computers & Mathematics with Applications
- Vol. 203, 56-72
An efficient reduced-order approximation for the stochastic Allen-Cahn equation
- 5 December 2025
- Published by Elsevier in Computers & Mathematics with Applications
- Vol. 203, 56-72
Open AccessAn efficient reduced-order approximation for the stochastic Allen-Cahn equation
- 19 September 2025
- Published by Springer Nature in Communications on Applied Mathematics and Computation
- Vol. 8 (5) , 1-20
Strong Approximation of Stochastic Subdiffusion Driven by Integrated Multiplicative Space-Time White Noise
- 19 September 2025
- Published by Springer Nature in Communications on Applied Mathematics and Computation
- Vol. 8 (5) , 1-20
Strong Approximation of Stochastic Subdiffusion Driven by Integrated Multiplicative Space-Time White Noise
- Open Access
- 1 September 2025
- Published by Taylor & Francis in Diabetes, Metabolic Syndrome and Obesity
- Vol. ume 18, 3427-3445
Obesity and Its Comorbidities: Current Treatment Options, Emerging Biological Mechanisms, Future Perspectives and Challenges
Obesity is a chronic, multifactorial disease and a major global public health challenge. Defined by excessive fat accumulation, obesity significantly increases the risk of numerous diseases, including type 2 diabetes mellitus (T2DM), cardiovascular disease, heart failure, and metabolic dysfunction-associated steatotic liver disease, contributing to rising morbidity and mortality rates worldwide. Although several pharmacological treatments have demonstrated notable efficacy in weight management, concerns regarding drug safety remain a significant challenge. Metabolic bariatric surgery (MBS) has emerged as the most effective intervention for achieving long-term and sustained weight loss; however, it is typically reserved for advanced stages of the disease. Moreover, the role of MBS in managing obesity-related comorbidities remains a topic of ongoing debate. In this review, we provide a comprehensive analysis of the epidemiology of obesity and its associated comorbidities, along with the latest insights into the mechanisms underlying obesity-induced chronic complications. Growing evidence highlights the crucial role of imbalances between white and brown adipose tissues, alterations in gut microbiota, genetic and epigenetic modifications, and immune system dysregulation in driving obesity and its related conditions. These emerging insights have unveiled numerous potential therapeutic targets with promising weight-reducing effects. Furthermore, advancements in our understanding of signal transduction pathways may pave the way for future multimodal therapeutic strategies in obesity management, ushering in a new era of precision medicine.
- 1 September 2025
- Published by Taylor & Francis in Diabetes, Metabolic Syndrome and Obesity
- Vol. ume 18, 3427-3445
Open AccessObesity and Its Comorbidities: Current Treatment Options, Emerging Biological Mechanisms, Future Perspectives and Challenges
Obesity is a chronic, multifactorial disease and a major global public health challenge. Defined by excessive fat accumulation, obesity significantly increases the risk of numerous diseases, including type 2 diabetes mellitus (T2DM), cardiovascular disease, heart failure, and metabolic dysfunction-associated steatotic liver disease, contributing to rising morbidity and mortality rates worldwide. Although several pharmacological treatments have demonstrated notable efficacy in weight management, concerns regarding drug safety remain a significant challenge. Metabolic bariatric surgery (MBS) has emerged as the most effective intervention for achieving long-term and sustained weight loss; however, it is typically reserved for advanced stages of the disease. Moreover, the role of MBS in managing obesity-related comorbidities remains a topic of ongoing debate. In this review, we provide a comprehensive analysis of the epidemiology of obesity and its associated comorbidities, along with the latest insights into the mechanisms underlying obesity-induced chronic complications. Growing evidence highlights the crucial role of imbalances between white and brown adipose tissues, alterations in gut microbiota, genetic and epigenetic modifications, and immune system dysregulation in driving obesity and its related conditions. These emerging insights have unveiled numerous potential therapeutic targets with promising weight-reducing effects. Furthermore, advancements in our understanding of signal transduction pathways may pave the way for future multimodal therapeutic strategies in obesity management, ushering in a new era of precision medicine.
- Open Access
- 25 April 2025
- Published by Elsevier in Communications in Nonlinear Science and Numerical Simulation
- Vol. 148
Strong convergence for efficient full discretization of the stochastic Allen–Cahn equation with multiplicative noise
- 25 April 2025
- Published by Elsevier in Communications in Nonlinear Science and Numerical Simulation
- Vol. 148
Open AccessStrong convergence for efficient full discretization of the stochastic Allen–Cahn equation with multiplicative noise
- 6 September 2024
- Published by Springer Nature in Fractional Calculus and Applied Analysis
- Vol. 27 (5) , 2754-2780
An efficient numerical method to the stochastic fractional heat equation with random coefficients and fractionally integrated multiplicative noise
- 6 September 2024
- Published by Springer Nature in Fractional Calculus and Applied Analysis
- Vol. 27 (5) , 2754-2780
An efficient numerical method to the stochastic fractional heat equation with random coefficients and fractionally integrated multiplicative noise