Associate Professor William   McLean
Associate Professor

Associate Professor William McLean

Science
Sch of Mathematics & Statistic

RESEARCH INTERESTS

  • Computational mathematics;
  • integral equations;
  • nonlocal evolution equations

ADMINISTRATIVE DUTIES

School Records System Manager, Maths & Stats.

TEACHING DUTIES

  • Math3101/5305 Computational Mathematics
  • Math2019 Engineering Mathematics 2E

EXTERNAL

Editorial Board of SIAM Journal on Numerical Analysis and the Journal of Integral Equations and Applications.

Phone
9385 7045
Location
The School of Mathematics and Statistics University of New South Wales SYDNEY NSW 2052 The Red Centre Room 2085

Publications

  • Book Chapters | 2019
    Associate Professor William McLean
    McLean W, 2019, 'Wider Contours and Adaptive Contours', in 2017 MATRIX Annals, pp. 79 - 98, http://dx.doi.org/10.1007/978-3-030-04161-8_7
    Book Chapters | 2018
    Associate Professor William McLean
    McLean W, 2018, 'Exponential sum approximations for t−β', in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, Springer, pp. 911 - 930, http://dx.doi.org/10.1007/978-3-319-72456-0_40
    Books | 2000
    Associate Professor William McLean
    Mclean W, 2000, Strongly elliptic systems and boundary integral equations, Original, Cambridge University Press, UK
    Book Chapters | 1989
    Associate Professor William McLean
    McLean W; Wendland WL, 1989, 'Trigonometric Approximation of Solutions of Periodic Pseudodifferential Equations', in The Gohberg Anniversary Collection, Birkhäuser Basel, pp. 359 - 383, http://dx.doi.org/10.1007/978-3-0348-9278-0_20
    Book Chapters | 1989
    Associate Professor William McLean
    McLean W; Wendland WL, 1989, 'Trigonometric Approximation of Solutions of Periodic Pseudodifferential Equations', in The Gohberg Anniversary Collection, Birkhäuser Basel, pp. 851 - 875, http://dx.doi.org/10.1007/978-3-0348-9144-8_37
  • Journal articles | 2021
    Associate Professor William McLean
    Liao HL; McLean W; Zhang J, 2021, 'A second-order scheme with nonuniform time steps for a linear reaction-subdiffusion problem', Communications in Computational Physics, vol. 30, pp. 567 - 601, http://dx.doi.org/10.4208/CICP.OA-2020-0124
    Journal articles | 2021
    Associate Professor William McLean
    McLean W; Mustapha K, 2021, 'Uniform stability for a spatially discrete, subdiffusive Fokker-Planck equation', NUMERICAL ALGORITHMS, http://dx.doi.org/10.1007/s11075-021-01160-3
    Journal articles | 2021
    Associate Professor William McLean
    Banz L; Ilyas M; Lamichhane BP; McLean W; Stephan EP, 2021, 'A mixed finite element method for the Poisson problem using a biorthogonal system with Raviart–Thomas elements', Numerical Methods for Partial Differential Equations, vol. 37, pp. 2429 - 2445, http://dx.doi.org/10.1002/num.22722
    Journal articles | 2021
    Associate Professor William McLean
    McLean W, 2021, 'Numerical evaluation of Mittag-Leffler functions', Calcolo, vol. 58, http://dx.doi.org/10.1007/s10092-021-00398-6
    Journal articles | 2021
    Associate Professor William McLean
    McLean W; Mustapha K; Ali R; Knio OM, 2021, 'Erratum to “Regularity theory for time-fractional advection-diffusion-reaction equations” [Comput. Math. Appl. 79 (2020) 947–961] (Computers and Mathematics with Applications (2020) 79(4) (947–961), (S0898122119304055), (10.1016/j.camwa.2019.08.008))', Computers and Mathematics with Applications, vol. 85, pp. 82 - 83, http://dx.doi.org/10.1016/j.camwa.2021.01.008
    Journal articles | 2020
    Associate Professor William McLean
    McLean W; Mustapha K; Ali R; Knio OM, 2020, 'Regularity theory for time-fractional advection–diffusion–reaction equations', Computers and Mathematics with Applications, vol. 79, pp. 947 - 961, http://dx.doi.org/10.1016/j.camwa.2019.08.008
    Journal articles | 2020
    Associate Professor William McLean
    McLean W, 2020, 'IMPLEMENTATION of HIGH-ORDER, DISCONTINUOUS GALERKIN TIME STEPPING for FRACTIONAL DIFFUSION PROBLEMS', ANZIAM Journal, vol. 62, pp. 121 - 147, http://dx.doi.org/10.1017/S1446181120000152
    Journal articles | 2019
    Associate Professor William McLean
    Liao HL; McLean W; Zhang J, 2019, 'A discrete Grönwall inequality with applications to numerical schemes for subdiffusion problems', SIAM Journal on Numerical Analysis, vol. 57, pp. 218 - 237, http://dx.doi.org/10.1137/16M1175742
    Journal articles | 2019
    Associate Professor William McLean
    Le KN; McLean W; Stynes M, 2019, 'Existence, uniqueness and regularity of the solution of the time-fractional Fokker–Planck equation with general forcing', Communications on Pure and Applied Analysis, vol. 18, pp. 2765 - 2787, http://dx.doi.org/10.3934/cpaa.2019124
    Journal articles | 2019
    Associate Professor William McLean
    McLean W; Mustapha K; Ali R; Knio O, 2019, 'Well-posedness of time-fractional advection-diffusion-reaction equations', Fractional Calculus and Applied Analysis, vol. 22, pp. 918 - 944, http://dx.doi.org/10.1515/fca-2019-0050
    Journal articles | 2018
    Associate Professor William McLean
    Le KN; Mclean W; Mustapha K, 2018, 'A semidiscrete finite element approximation of a time-fractional Fokker Planck equation with nonsmooth initial data', SIAM Journal on Scientific Computing, vol. 40, pp. A3831 - A3852, http://dx.doi.org/10.1137/17M1125261
    Journal articles | 2017
    Associate Professor William McLean
    Le KN; McLean W; Lamichhane B, 2017, 'FINITE ELEMENT APPROXIMATION of A TIME-FRACTIONAL DIFFUSION PROBLEM for A DOMAIN with A RE-ENTRANT CORNER', ANZIAM Journal, vol. 59, pp. 61 - 82, http://dx.doi.org/10.1017/S1446181116000365
    Journal articles | 2017
    Associate Professor William McLean
    Macnamara S; Henry B; McLean W, 2017, 'Fractional euler limits and their applications', SIAM Journal on Applied Mathematics, vol. 77, pp. 447 - 469, http://dx.doi.org/10.1137/16M1091861
    Journal articles | 2017
    Associate Professor William McLean
    Le KN; McLean W; Lamichhane B, 2017, 'Finite element approximation of a time-fractional diffusion problem for a domain with a re-entrant corner', ANZIAM Journal, vol. 59, pp. 61 - 61, http://dx.doi.org/10.21914/anziamj.v59i0.10940
    Journal articles | 2016
    Associate Professor William McLean
    Le KN; McLean W; Mustapha K, 2016, 'Numerical solution of the time-fractional Fokker-Planck equation with general forcing', SIAM Journal on Numerical Analysis, vol. 54, pp. 1763 - 1784, http://dx.doi.org/10.1137/15M1031734
    Journal articles | 2015
    Associate Professor William McLean
    McLean W; Mustapha K, 2015, 'Time-stepping error bounds for fractional diffusion problems with non-smooth initial data', Journal of Computational Physics, vol. 293, pp. 201 - 217, http://dx.doi.org/10.1016/j.jcp.2014.08.050
    Journal articles | 2014
    Associate Professor William McLean
    Le Gia QT; McLean W, 2014, 'Solving the heat equation on the unit sphere via Laplace transforms and radial basis functions', Advances in Computational Mathematics, vol. 40, pp. 353 - 375, http://dx.doi.org/10.1007/s10444-013-9311-6
    Journal articles | 2013
    Associate Professor William McLean
    Wang K; McLean W; Kampwerth H, 2013, 'Transient photoluminescence from silicon wafers: Finite element analysis', JOURNAL OF APPLIED PHYSICS, vol. 114, http://dx.doi.org/10.1063/1.4826896
    Journal articles | 2013
    Associate Professor William McLean
    Kim IS; McLean W, 2013, 'Computing the hausdorff distance between two sets of parametric curves', Communications of the Korean Mathematical Society, vol. 28, pp. 833 - 850, http://dx.doi.org/10.4134/CKMS.2013.28.4.833
    Journal articles | 2013
    Associate Professor William McLean
    Mustapha K; Mclean W, 2013, 'Superconvergence of a discontinuous Galerkin method for fractional diffusion and wave equations', SIAM Journal on Numerical Analysis, vol. 51, pp. 491 - 515, http://dx.doi.org/10.1137/120880719
    Journal articles | 2012
    Associate Professor William McLean
    Mclean W; Thomee V, 2012, 'Iterative solution of shifted positive-definitive linear systems arising in a numerical method for the heat equation based on Laplace transformation and quadrature', ANZIAM Journal, vol. 53, pp. 134 - 155, http://dx.doi.org/10.1017/S1446181112000107
    Journal articles | 2012
    Associate Professor William McLean
    Mustapha K; Mclean W, 2012, 'Uniform convergence for a discontinuous Galerkin, time-stepping method applied to a fractional diffusion equation', IMA Journal of Numerical Analysis, vol. 32, pp. 906 - 925, http://dx.doi.org/10.1093/imanum/drr027
    Journal articles | 2012
    Associate Professor William McLean
    Mclean W, 2012, 'Fast summation by interval clustering for an evolution equation with memory', SIAM Journal on Scientific Computing, vol. 34, pp. A3039 - A3056, http://dx.doi.org/10.1137/120870505
    Journal articles | 2012
    Associate Professor William McLean
    McLean W; Thomee V, 2012, 'Iterative solution of shifted positive-definite linear systems arising in a numerical method for the heat equation based on Laplace transformation and quadrature', ANZIAM Journal, vol. 53, pp. 134 - 134, http://dx.doi.org/10.21914/anziamj.v53i0.5248
    Journal articles | 2011
    Associate Professor William McLean
    Mclean W; Mustapha K, 2011, 'Piecewise-linear, discontinuous Galerkin method for a fractional diffusion equation', Numerical Algorithms, vol. 56, pp. 159 - 184, http://dx.doi.org/10.1007/s11075-010-9379-8
    Journal articles | 2011
    Associate Professor William McLean
    McLean W, 2011, 'Regularity of solutions to a time-fractional diffusion equation', ANZIAM Journal, vol. 52, pp. 123 - 138, http://dx.doi.org/10.1017/S1446181111000617
    Journal articles | 2010
    Associate Professor William McLean
    Mclean W; Thomee V, 2010, 'Maximum-norm error analysis of a numerical solution via Laplace transformation and quadrature of a fractional-order evolution equation', IMA Journal of Numerical Analysis, vol. 30, pp. 208 - 230, http://dx.doi.org/10.1093/imanum/drp004
    Journal articles | 2010
    Associate Professor William McLean
    Mclean W; Thomee V, 2010, 'Numerical solution via Laplace transforms of a fractional order evolution equation', Journal of Integral Equations and Applications, vol. 22, pp. 57 - 94, http://dx.doi.org/10.1216/JIE-2010-22-1-57
    Journal articles | 2009
    Associate Professor William McLean
    Mustapha KA; Mclean W, 2009, 'Discontinuous galerkin method for an evolution equation with a memory term of positive type', Mathematics of Computation, vol. 78, pp. 1975 - 1995, http://dx.doi.org/10.1090/S0025-5718-09-02234-0
    Journal articles | 2009
    Associate Professor William McLean
    Mustapha K; Mclean W, 2009, 'Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation', Numerical Algorithms, vol. 52, pp. 69 - 88, http://dx.doi.org/10.1007/s11075-008-9258-8
    Journal articles | 2007
    Associate Professor William McLean
    Mclean W; Mustapha K, 2007, 'A second-order accurate numerical method for a fractional wave equation', Numerische Mathematik, vol. 105, pp. 481 - 510, http://dx.doi.org/10.1007/s00211-006-0045-y
    Journal articles | 2006
    Associate Professor William McLean
    Graham IG; Mclean W, 2006, 'Anisotropic mesh refinement: the conditioning of Galerkin boundary element matrices and simple preconditioners', SIAM Journal on Numerical Analysis, vol. 44, pp. 1487 - 1513, http://dx.doi.org/10.1137/040621247
    Journal articles | 2005
    Associate Professor William McLean
    Mclean W; Sloan IH; Thomee V, 2005, 'Time discretization via Laplace transformation of an integro-differential equation of an integro-differential equation of parabolic type', Numerische Mathematik, vol. 102, pp. 497 - 522, http://dx.doi.org/10.1007/s00211-005-0657-7
    Journal articles | 2004
    Associate Professor William McLean
    Mclean W; Thomee V, 2004, 'Time discretization of an evolution equation via Laplace transforms', IMA Journal of Numerical Analysis, vol. 24, pp. 439 - 463, http://dx.doi.org/10.1093/imanum/24.3.439
    Journal articles | 2003
    Associate Professor William McLean
    Ainsworth M; Mclean W, 2003, 'Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes', Numerische Mathematik, vol. 93, pp. 387 - 413, http://dx.doi.org/10.1007/s002110100391
    Journal articles | 2003
    Associate Professor William McLean
    Jeon Y; Mclean W, 2003, 'A new boundary element method for the biharmonic equation with Dirichlet boundary conditions', Advances in Computational Mathematics, vol. 19, pp. 339 - 365, http://dx.doi.org/10.1023/A:1024206232212
    Journal articles | 2000
    Associate Professor William McLean
    Ainsworth M; Mclean W; Tran T, 2000, 'Diagonal scaling of stiffness matrices in the Galerkin boundary element method', Journal of Australian Mathematical Society B, vol. 42, pp. 141 - 150
    Journal articles | 1999
    Associate Professor William McLean
    Ainsworth M; Mclean W; Tran T, 1999, 'The conditioning of boundary element equations on locally refined meshes and preconditioning by diagonal scaling', SIAM Journal on Numerical Analysis, vol. 36, pp. 1901 - 1932, http://dx.doi.org/10.1137/S0036142997330809
    Journal articles | 1999
    Associate Professor William McLean
    Mclean W; Steinbach O, 1999, 'Boundary element preconditioners for a hypersingular integral equation on an interval', Advances in Computational Mathematics, vol. 11, pp. 271 - 286, http://dx.doi.org/10.1023/A:1018944530343
    Journal articles | 1997
    Associate Professor William McLean
    Mclean W; Thomee V, 1997, 'Asymptotic behaviour of numerical solutions of an evolution equation with memory', Asymptotic Analysis, vol. 14, pp. 257 - 276
    Journal articles | 1997
    Associate Professor William McLean
    Mclean W; Tran T, 1997, 'A preconditioning strategy of boundary element Galerkin methods', Numerical Methods for Partial Differential Equations, vol. 13, pp. 283 - 301, http://dx.doi.org/10.1002/(SICI)1098-2426(199705)13:3<283::AID-NUM4>3.0.CO;2-J
    Journal articles | 1996
    Associate Professor William McLean
    Mclean W; Thomee V; Wahlbin LB, 1996, 'Discretization with variable time steps of an evoloution equation with a positive type memory term', Journal of Computational and Applied Mathematics, vol. 69, pp. 49 - 69, http://dx.doi.org/10.1016/0377-0427(95)00025-9
    Journal articles | 1996
    Associate Professor William McLean
    Mclean W; Prossdorf S, 1996, 'Boundary element collocation methods using splines with multiple knots', Numerische Mathematik, vol. 74, pp. 419 - 451, http://dx.doi.org/10.1007/s002110050224
    Journal articles | 1994
    Associate Professor William McLean
    McLEAN W, 1994, 'Numerical evaluation of some trigonometric series', Mathematics of Computation, vol. 63, pp. 271 - 274, http://dx.doi.org/10.1090/S0025-5718-1994-1240661-6
    Journal articles | 1994
    Associate Professor William McLean
    McLean W, 1994, 'Fully-discrete collocation methods for an integral equation of the first kind', Journal of Integral Equations and Applications, vol. 6, pp. 537 - 571, http://dx.doi.org/10.1216/jiea/1181075835
    Journal articles | 1994
    Associate Professor William McLean
    Mclean W; Sloan IH, 1994, 'A fully discrete and symmetric boundary element method', IMA Journal of Numerical Analysis, vol. 14, pp. 311 - 345, http://dx.doi.org/10.1093/imanum/14.3.311
    Journal articles | 1994
    Associate Professor William McLean
    MCLEAN W, 1994, 'NUMERICAL EVALUATION OF SOME TRIGONOMETRIC SERIES', MATHEMATICS OF COMPUTATION, vol. 63, pp. 271 - 275, http://dx.doi.org/10.2307/2153573
    Journal articles | 1993
    Associate Professor William McLean
    MCLEAN W; THOMEE V, 1993, 'NUMERICAL-SOLUTION OF AN EVOLUTION EQUATION WITH A POSITIVE-TYPE MEMORY TERM', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES B-APPLIED MATHEMATICS, vol. 35, pp. 23 - 70, http://dx.doi.org/10.1017/S0334270000007268
    Journal articles | 1993
    Associate Professor William McLean
    McLean W; Prössdorf S; Wendland WL, 1993, 'A fully-discrete trigonometric collocation method', Journal of Integral Equations and Applications, vol. 5, pp. 103 - 129, http://dx.doi.org/10.1216/jiea/1181075730
    Journal articles | 1992
    Associate Professor William McLean
    Costabel M; McLean W, 1992, 'Spline collocation for strongly elliptic equations on the torus', Numerische Mathematik, vol. 62, pp. 511 - 538, http://dx.doi.org/10.1007/BF01396241
    Journal articles | 1991
    Associate Professor William McLean
    McLean W, 1991, 'Local and Global Descriptions of Periodic Pseudodifferential Operators', Mathematische Nachrichten, vol. 150, pp. 151 - 161, http://dx.doi.org/10.1002/mana.19911500112
    Journal articles | 1990
    Associate Professor William McLean
    MCLEAN W, 1990, 'AN INTEGRAL-EQUATION METHOD FOR A PROBLEM WITH MIXED BOUNDARY-CONDITIONS', SIAM JOURNAL ON MATHEMATICAL ANALYSIS, vol. 21, pp. 917 - 934, http://dx.doi.org/10.1137/0521051
    Journal articles | 1989
    Associate Professor William McLean
    McLean W; Prößdorf SB; Wendland WL, 1989, 'Pointwise error estimates for the trigonometric collocation method applied to singular integral equations and periodic Pseudodifferential equations', Journal of Integral Equations and Applications, vol. 2, pp. 125 - 146, http://dx.doi.org/10.1216/JIE-1989-2-1-125
    Journal articles | 1989
    Associate Professor William McLean
    Mclean W, 1989, 'Asymptotic error expansions for numerical solutions of integral equations', IMA Journal of Numerical Analysis, vol. 9, pp. 373 - 384, http://dx.doi.org/10.1093/imanum/9.3.373
    Journal articles | 1988
    Associate Professor William McLean
    McLean W; Elliott D, 1988, 'On the p-norm of the truncated Hilbert transform', Bulletin of the Australian Mathematical Society, vol. 38, pp. 413 - 420, http://dx.doi.org/10.1017/S0004972700027799
    Journal articles | 1988
    Associate Professor William McLean
    McLean W, 1988, 'Hölder estimates for the Cauchy integral on a Lipschitz contour', Journal of Integral Equations and Applications, vol. 1, pp. 435 - 451, http://dx.doi.org/10.1216/JIE-1988-1-3-435
    Journal articles | 1986
    Associate Professor William McLean
    McLean W, 1986, 'A spectral Galerkin method for a boundary integral equation', Mathematics of Computation, vol. 47, pp. 597 - 607, http://dx.doi.org/10.1090/S0025-5718-1986-0856705-2
    Journal articles | 1986
    Associate Professor William McLean
    MCLEAN W, 1986, 'A SPECTRAL GALERKIN METHOD FOR A BOUNDARY INTEGRAL-EQUATION', MATHEMATICS OF COMPUTATION, vol. 47, pp. 597 - 607, http://dx.doi.org/10.2307/2008175
  • Patents | 2015
    Associate Professor William McLean
    Kampwerth H; Wang KW; MCLEAN , 2015, A method and apparatus for testing the performance of a semiconductor material, Patent No. , Patent Agent:Griffithhack
    Conference Papers | 2013
    Associate Professor William McLean
    wang K; Kampwerth H; McLean W, 2013, 'Time-resolved Photoluminescence of Silicon Wafers for Illumination Source with High Repetition Rate: Finite Element Solution', in Proceedings of the 28th European Photovoltaic Solar Energy Conference and Exhibition, 28th European Photovoltaic Solar Energy Conference and Exhibition, Villepinte, Frankreich, pp. 1622 - 1626, presented at 28th European Photovoltaic Solar Energy Conference and Exhibition, Villepinte, Frankreich, 23 September 2013 - 26 September 2013, http://dx.doi.org/10.4229/28thEUPVSEC2013-2CV.3.52
    Conference Papers | 2010
    Associate Professor William McLean
    Le Gia QT; Mclean W, 2010, 'Numerical solution of a parabolic equation on the sphere using Laplace transforms and radial basis functions', in ANZIAM Journal, Australian Mathematics Publishing Association Inc, Canberra, ACT, Australia, pp. C89 - C102, presented at CTAC 2010, UNSW, Sydney, 28 November 2010 - 01 December 2010
    Conference Papers | 1995
    Associate Professor William McLean
    McLean W; Prossdorf S, 1995, 'Boundary element collocation methods with reduced inter-element smoothness', in Morino L; Wendland WL (ed.), IABEM SYMPOSIUM ON BOUNDARY INTEGRAL METHODS FOR NONLINEAR PROBLEMS, KLUWER ACADEMIC PUBL, PONTIGNANO, ITALY, pp. 155 - 160, presented at IABEM Symposium on Boundary Integral Methods for Nonlinear Problems, PONTIGNANO, ITALY, 28 May 1995 - 03 June 1995, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1997BJ28U00024&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 1984
    Associate Professor William McLean
    McLean W, 1984, 'EFFECT OF APPROXIMATING THE GEOMETRY FOR A SIMPLE BOUNDARY INTEGRAL EQUATION.', in EFFECT OF APPROXIMATING THE GEOMETRY FOR A SIMPLE BOUNDARY INTEGRAL EQUATION., pp. 277 - 288

Awards

Grants

Media