Associate Professor Yubin Yan

Dr. Yubin Yan brings over two decades of teaching experience in mathematics to both undergraduate and graduate students at UK universities.

His expertise spans a wide array of modules, including but not limited to analysis, linear algebra, geometry, stochastic calculus, numerical analysis, numerical methods for differential equations, complex analysis, functional analysis, partial differential equations, fractional calculus and fractional differential equation, group theory, stochastic calculus, stochastic differential equation and the foundation of mathematics.

Dr. Yan's dedication to teaching excellence and his comprehensive understanding of mathematical concepts enrich the learning experiences of his students across various levels of study

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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.