In this paper,we study a high-order compact difference scheme for the fourth-order fractional subdiffusion system.We consider the situation in which the unknown function and its first-order derivative are given at the...In this paper,we study a high-order compact difference scheme for the fourth-order fractional subdiffusion system.We consider the situation in which the unknown function and its first-order derivative are given at the boundary.The scheme is shown to have high order convergence.Numerical examples are given to verify the theoretical results.展开更多
We present the finite difference/element method for a two-dimensional modified fractional diffusion equation.The analysis is carried out first for the time semi-discrete scheme,and then for the full discrete scheme.Th...We present the finite difference/element method for a two-dimensional modified fractional diffusion equation.The analysis is carried out first for the time semi-discrete scheme,and then for the full discrete scheme.The time discretization is based on the L1-approximation for the fractional derivative terms and the second-order backward differentiation formula for the classical first order derivative term.We use finite element method for the spatial approximation in full discrete scheme.We show that both the semi-discrete and full discrete schemes are unconditionally stable and convergent.Moreover,the optimal convergence rate is obtained.Finally,some numerical examples are tested in the case of one and two space dimensions and the numerical results confirm our theoretical analysis.展开更多
Advances in nanotechnology enable scientists for the first time to study biological pro-cesses on a nanoscale molecule-by-molecule basis.They also raise challenges and opportunities for statisticians and applied proba...Advances in nanotechnology enable scientists for the first time to study biological pro-cesses on a nanoscale molecule-by-molecule basis.They also raise challenges and opportunities for statisticians and applied probabilists.To exemplify the stochastic inference and modeling problems in the field,this paper discusses a few selected cases,ranging from likelihood inference,Bayesian data augmentation,and semi-and non-parametric inference of nanometric biochemical systems to the uti-lization of stochastic integro-differential equations and stochastic networks to model single-molecule biophysical processes.We discuss the statistical and probabilistic issues as well as the biophysical motivation and physical meaning behind the problems,emphasizing the analysis and modeling of real experimental data.展开更多
基金the Macao Science and Technology Development Fund FDCT/001/2013/A and the grant MYRG086(Y2-L2)-FST12-VSW from the University of Macao.
文摘In this paper,we study a high-order compact difference scheme for the fourth-order fractional subdiffusion system.We consider the situation in which the unknown function and its first-order derivative are given at the boundary.The scheme is shown to have high order convergence.Numerical examples are given to verify the theoretical results.
基金This research was partly supported by the National Basic Research Program of China973 Program under Grant No.2011CB706903+3 种基金the Program for New Century Excellent Talents in University under Grant No.NCET-09-0438the National Natural Science Foundation of China under Grant No.10801067the Fundamental Research Funds for the Central Universities under Grant No.lzujbky-2010-63No.lzujbky-2012-k26。
文摘We present the finite difference/element method for a two-dimensional modified fractional diffusion equation.The analysis is carried out first for the time semi-discrete scheme,and then for the full discrete scheme.The time discretization is based on the L1-approximation for the fractional derivative terms and the second-order backward differentiation formula for the classical first order derivative term.We use finite element method for the spatial approximation in full discrete scheme.We show that both the semi-discrete and full discrete schemes are unconditionally stable and convergent.Moreover,the optimal convergence rate is obtained.Finally,some numerical examples are tested in the case of one and two space dimensions and the numerical results confirm our theoretical analysis.
基金supported by the United States National Science Fundation Career Award (Grant No. DMS-0449204)
文摘Advances in nanotechnology enable scientists for the first time to study biological pro-cesses on a nanoscale molecule-by-molecule basis.They also raise challenges and opportunities for statisticians and applied probabilists.To exemplify the stochastic inference and modeling problems in the field,this paper discusses a few selected cases,ranging from likelihood inference,Bayesian data augmentation,and semi-and non-parametric inference of nanometric biochemical systems to the uti-lization of stochastic integro-differential equations and stochastic networks to model single-molecule biophysical processes.We discuss the statistical and probabilistic issues as well as the biophysical motivation and physical meaning behind the problems,emphasizing the analysis and modeling of real experimental data.
