Dr Yubin Yan

Programme Leader in BSc Mathematics Associate Professor in Mathematics

+44 (0) 1244 513355
School of Computing and Engineering Sciences
y.yan@chester.ac.uk
Dr Yubin Yan

Yubin graduated from Shanxi Normal University,  P.R. China in 1985 with a BSc in Mathematics. He went on to obtain his MSc in Mathematics in 1991 from Harbin institute of Technology, P. R. China and completed his PhD in Mathematics in 2003 from Chalmers University of Technology, Sweden.

Yubin joined the University of Chester in September 2007 as a lecturer in Mathematics. After one year, he was promoted to a senior lecturer position in the Maths Department.

Before he joined Chester in 2007, he was a research associate in the Department of Automatic Control and System Engineering at the University of Sheffield (from 2004 to 2007), and a research associate in the Department of Mathematics at the University of Manchester (from 2003 to 2004). 

Yubin enjoys teaching Mathematics very much. He also enjoys learning Mathematics and working with people.

Memberships and Affiliations

  • Member of the Society for Industrial and Applied Mathematics
  • Reviewer for Mathematical Reviews
  • Editorial board in the Journal of  Franklin Institute
  • Referee for Journals: IMA J. Numerical Mathematics, BIT, Journal Computational Physics, Applied Mathematics and Computation, International Journal of System Science, SIAM Journal of Numerical Analysis
  • Reviewer of EPSRC research grants

Undergraduate Level

At level 4, Yubin teaches pure mathematics. At level 5, he teaches Analysis and Complex Algebra, Geometry, and MATLAB. At level 6, Yubin is responsible for Real and Complex Function Theory, Numerical Analysis, Numerical methods: stability and convergence, Partial Differential Equations. 

Postgraduate Level

Yubin teaches Advanced Partial Differential Equations, Numerical Methods: Stability and Convergence, Stochastic Partial differential Equations, Fractional partial differential Equations. 

Yubin’s research interests are concerned with numerical methods for nonlinear partial differential equations (both in deterministic and stochastic), numerical methods for  fractional partial differential equations,  the finite element method, stability analysis and controllability for semilinear parabolic  systems, and the Navier-Stokes equation. 

Yubin is currently joint supervisor on several PhD projects. Successful past Phd supervision includes: 

  • Md. Abdul Malique, 2008--2012, Numerical treatment of oscillatory functional differential equations, Supervisors:  Dr. Yubin Yan (10%) Prof. Neville Ford (90%)

  • Kamal Kanti Pal, 2011-2015,  Supervisors: Dr. Yubin Yan (90%) Prof. Neville Ford (10%)

  • Nicci Banks, 2008-2015, Supervisors: Dr. Yubin Yan (10%),  Prof. Neville Ford (90%)

  • Mozorul Khan, 2012-present, Supervisors Dr. Yubin Yan (90%), Prof. Neville Ford (10%)

PhD Thesis (2003)

  • Chalmers University of Technology, Sweden (With Profs: Stig Larsson and Vidar Thomee)

Title: Error analysis and smoothing properties of discretized deterministic and stochastic parabolic problems.

Articles

(with  R. Du and Z. Liang), A high-order scheme to approximate the Caputo fractional derivative and its application to solve the fractional diffusion wave equation, Journal of Computational Physics, (2018).

(with Z. Li), Error estimates of high-order numerical methods for solving time fractional partial differential equations, Fractional Calculus and Applied Analysis, (2018).

(with Y. Xing),  A higher order numerical method for time fractional partial differential equations with non-smooth data, Journal of Computational physics, 357(2018), 305-323.

(with   M. Khan and N. J. Ford), An analysis of the modified L1 scheme for time-fractional partial differential equations with non-smooth data, SIAM Journal on Numerical Analysis, 56(2018), 210-227. 

(with M. S. Asl  and  M. Javidi), A novel high-order algorithm for the numerical estimation of fractional differential equations, J. of Computational and Applied Mathematics, 342(2018), 180-201

(with Y. Liu and J. Roberts), A note on finite difference methods for nonlinear fractional differential equations with non-uniform meshes, International Journal of Computer Mathematics, 95(2018), 1151-1169.

(with Y. Liu and J. Roberts), Detailed error analysis for a fractional Adams method with graded meshes,  Numer. Algor. 78(2018), 1195-1216.

(with Neville J. Ford), An approach to construct higher order time discretisation schemes for time  fractional partial differential equations, Fract. Calc. Appl. Anal., 20(2017), 1076-1105.

(with Y. Yang and  Neville. J. Ford, Some time stepping methods for fractional diffusion problems with nonsmooth data, Comput. Methods Appl. Math., (18)2018, 129-146.

(with F. Liu and M. Khan), “Fourier spectral methods for stochastic space fractional partial differential equations driven by special additive noises”, Journal of Computational Analysis and Applications, 24(2018), 290-309.

(with Y. Liu and M. Khan), Discontinuous Galerkin time stepping method for solving linear space fractional partial differential equations, Applied Numerical Mathematics, 115 (2017), 200-213.

(with Z. Li and Z. Liang), High-Order Numerical Methods for Solving Time Fractional Partial Differential Equations, Journal of Scientific Computing, 71(2017), 785-803.

(with Y. Liu and M. Khan), Fourier Spectral Methods for Some Linear Stochastic Space-Fractional Partial Differential Equations, Mathematics, (4) 2016, doi:10.3390/math4030045.

(with Z. Li  and N. J. Ford), Error estimates of a high order numerical method for solving linear fractional differential equations, Applied Numerical Mathematics, 114 (2017), 201-220.

(with N. I. ~Kavallaris), Finite-time blow-up of a non-local stochastic parabolic problem, 2015, arXiv:1508.05496.

(with N. I. ~Kavallaris), A time discretization scheme for a nonlocal degenerate problem modelling resistance spot welding, Mathematical Modelling of Natural Phenomena, (10) 2015,90-112.

(with N. J. Ford and K. ~Pal), An algorithm for the numerical solution of space-fractional partial differential equations, Computational Methods in Applied Mathematics, (15)2015, 497-514.

(with P. Kamal and F. Liu), Numerical Solutions of Fractional Differential Equations by Extrapolation, Lecture Notes in Computer Science V. 9045, 2015, Springer, 291-299.

(with P. Kamal and F. Liu and G. Roberts), Finite Difference Method for Two-sided Space-fractional Partial Differential Equations,  Lecture Notes in Computer Science V. 9045, 2015, Springer, 299-307.

(with G. Zhang, W. Feng), Existence of time periodic solutions for a class of non-resonant discrete wave equations,  Advances in Difference Equations, (2015)  2015:120,  DOI 10.1186/s13662-015-0457-z

(with Z Liang and G Cai), “A dufort-Frankel difference scheme for two- dimensional sine-Gordon equation”, Discrete Dynamics in Nature and Society, 2014(2014), 1-22.

(with K Pal and N. J Ford), “Higher order numerical methods for solving fractional differential equations”, BIT Numer Math, 54(2014), 555-584, DOI 10.1007/s10543-013-0443-3.

(with N. J. Ford, M. M. Rodrigues and J. Xiao), “Numerical analysis of a two-parameter fractional telegraph equation”, Journal of Computational and Applied Mathematics, 249(2013), 95-106.

(with N. J. Ford and J. Xiao), “Stability of a numerical method for space-time-fractional telegraph equation”, Computational Methods in Applied Mathematics, 12(2012), 1-16.

(with E. N. Ekaka-a), “Stabilizing a mathematical model of plant species Interaction”, Journal of Franklin Institute, 348(2011), 2744-2758.

(with N. J. Ford and J. Xiao), “A finite element method for the time fractional partial differential equations”,   Calc. Appl. Anal., 14(2011), 454-474

(with J. M. Ferreira, N. J. Ford, Md. Malique and S. Pinelas), “Analytical and numerical treatment of oscillatory mixed differential equations with differentiable delays and advances”, Journal of Computational and Applied Mathematics, 235(2011), 5112-5130.

(with N. J. Ford and Md. Malique), “Numerical treatment of oscillatory functional differential equations”, Journal of Computational and Applied Mathematics, 234(2010), 2757-2767.

(with D. Coca and V. Barbu), “Finite-dimensional controller design for semilinear parabolic systems”, Nonlinear Analysis: Theory, methods and Applications, 70(2009), 4451-4475.

(with D. Coca and V. Barbu), “Feedback control for Navier-Stokes equation”, Nonlinear Functional Analysis and optimization, 29(2008), 225-242.

“Postprocessing the finite element method for semilinear parabolic Problems”, SIAM J. Numer. Anal., 44(2006), 1681-1702.

(with T. Shardlow), “Geometric ergodicity for dissipative particle dynamics”, Stochastic and Dynamics, 6(2006), 123-154.

(with V. Barbu and D. Coca), “Stabilizing semilinear parabolic equations”, Numerical Functional Analysis and Optimization, 26(2005), 449-480.

“Galerkin finite element methods for stochastic parabolic partial differential equations”, SIAM J. Numer. Anal., 43(2005), 1363-1384.

“Smoothing properties and approximation of time derivatives in multistep backward difference Methods for parabolic equations”, International Journal of Mathematics and Mathematics Sciences, 4(2005), 523-536.

“Semidiscrete Galerkin approximation for a linear stochastic parabolic partial differential equation driven by an additive noise”, BIT, 44(2004), 829-847.

“Smoothing properties and approximation of time derivatives for parabolic equations: constant time step”, IMA J. Numer. Anal., 23(2003), 465-487.

“Smoothing properties and approximation of time derivatives for parabolic equations: variable time step”, BIT, 43(2003), 647-669.

(with Z. Kang), “The analytic solution of the integral equation of renewal theory, (in Chinese)”, Chinese J. Appl. Probab. Statist., 16 (2000), No. 2, 125-132.

(with C. Li), “An expression for solutions of ill-posed operator equations of the first kind, (in Chinese)”, Acta Math. Sci., 18 (1998), No. 3, 264-269.

(with M. Cui and C. Li), “The representation of the solutions of operator equations Au = f”, Numer. Math. J. Chinese Univ., 17 (1995), No. 1, 82-86.

(with B. Liang and M. Cui), “An analytic expression for the renewal function”, (in Chinese), Heilongjiang Daxue Ziran Kexue Xuebo, 11 (1994), No. 3, 39-42.

(with M. Cui),  “The exact solution of the second kind Volterra integral equation” (in Chinese), No. Math. J. Chinese Univ., 15 (1993), No. 4, 291-296. 

Conference Papers

(with D. Coca and V. Barbu), “Internal stabilization for the parabolic system”, European Control Conference, Greek, Greece, 2007.