12 papers
High-order smoothness and high-order collocation approximation for Volterra integral equation with multiscale and nonlinear exponent kernel
Wenlin Qiu, Chuanwei Su, Xiangcheng Zheng
We consider a Volterra integral equation with multiscale and nonlinear exponent kernel. We propose the high-order smoothing conditions, under which the initial singularity of the s…
Multiscale solution decomposition of nonlocal-in-time problems with application in numerical computation
Mengmeng Liu, Jie Ma, Wenlin Qiu +1
This work develops a multiscale solution decomposition (MSD) method for nonlocal-in-time problems to separate a series of known terms with multiscale singularity from the original…
Long-time error estimate and decay of finite element method to a generalized viscoelastic flow
Yingwen Guo, Yinnian He, Wenlin Qiu +1
This work analyzes the finite element approximation to a viscoelastic flow model, which generalizes the Navier-Stokes equation and Oldroyd's model by introducing the tempered power…
Numerical analysis for subdiffusion problem with non-positive memory
Wenlin Qiu, Xiangcheng Zheng
This work considers the subdiffusion problem with non-positive memory, which not only arises from physical laws with memory, but could be transformed from sophisticated models such…
Finite difference method for nonlinear damped viscoelastic Euler-Bernoulli beam model
Wenlin Qiu, Xiangcheng Zheng, Tao Guo +1
We propose and analyze the numerical approximation for a viscoelastic Euler-Bernoulli beam model containing a nonlinear strong damping coefficient. The finite difference method is…
Compact difference method for Euler-Bernoulli beams and plates with nonlinear nonlocal strong damping
Tao Guo, Yiqun Li, Wenlin Qiu
We investigate the numerical approximation to the Euler-Bernoulli (E-B) beams and plates with nonlinear nonlocal strong damping, which describes the damped mechanical behavior of b…
Optimal control of variable-exponent subdiffusion
Yiqun Li, Mengmeng Liu, Wenlin Qiu
This work investigates the optimal control of the variable-exponent subdiffusion, which extends the work [Gunzburger and Wang, SIAM J. Control Optim. 2019] to the variable-exponent…
Numerical approximations for a hyperbolic integrodifferential equation with a non-positive variable-sign kernel and nonlinear-nonlocal damping
Wenlin Qiu, Xiangcheng Zheng, Kassem Mustapha
This work considers the Galerkin approximation and analysis for a hyperbolic integrodifferential equation, where the non-positive variable-sign kernel and nonlinear-nonlocal dampin…
A multiscale Abel kernel and application in viscoelastic problem
Wenlin Qiu, Tao Guo, Yiqun Li +2
We consider the variable-exponent Abel kernel and demonstrate its multiscale nature in modeling crossover dynamics from the initial quasi-exponential behavior to long-term power-la…
Generalizing subdiffusive Black-Scholes model by variable exponent: Model transformation and numerical approximation
Meihui Zhang, Yaxue Liu, Mengmeng Liu +2
This work generalizes the subdiffusive Black-Scholes model by introducing the variable exponent in order to provide adequate descriptions for the option pricing, where the variable…
Numerical analysis of high-order methods for variable-exponent fractional diffusion-wave equation
Wenlin Qiu, Xiangcheng Zheng
This work considers the variable-exponent fractional diffusion-wave equation, which describes, e.g. the propagation of mechanical diffusive waves in viscoelastic media with varying…
Local modification of subdiffusion by initial Fickian diffusion: Multiscale modeling, analysis and computation
Xiangcheng Zheng, Yiqun Li, Wenlin Qiu
We propose a local modification of the standard subdiffusion model by introducing the initial Fickian diffusion, which results in a multiscale diffusion model. The developed model…