Select Publications

Journal articles

McLean W, 2018, 'Exponential sum approximations for t', Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, pp. 911 - 930, http://dx.doi.org/10.1007/978-3-319-72456-0_40

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

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

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

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

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

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

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

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

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

McLean W, 2012, 'Fast summation by interval clustering for an evolution equation with memory', SIAM Journal on Scientific Computing, vol. 34, http://dx.doi.org/10.1137/120870505

Mustapha K;McLean W, 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

Mclean W;Thomée V, 2011, '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 - 155, http://dx.doi.org/10.1017/S1446181112000107

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

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

McLean W;Thomée 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

McLean W;Mustapha K, 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

Mustapha K;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

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

McLean W;Sloan IH;Thomée V, 2006, 'Time discretization via Laplace transformation 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

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

McLean W;Thomée 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

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

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 - 354, http://dx.doi.org/10.1023/A:1024206232212

Ainsworth M;Mclean B;Tran T, 2000, 'Diagonal scaling of stiffness matrices in the galerkin boundary element method', ANZIAM Journal, vol. 42, pp. 141 - 150

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

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

McLean W;Thomée V, 1997, 'Asymptotic behaviour of numerical solutions of an evolution equation with memory', Asymptotic Analysis, vol. 14, pp. 257 - 276

McLean W;Tran T, 1997, 'A Preconditioning Strategy for 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

McLean W;Thomée V;Wahlbin LB, 1996, 'Discretization with variable time steps of an evolution 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

McLean W;Prößdorf SB, 1996, 'Boundary element collocation methods using splines with multiple knots', Numerische Mathematik, vol. 74, pp. 419 - 451, http://dx.doi.org/10.1007/s002110050224

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

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

MCLEAN W, 1994, 'NUMERICAL EVALUATION OF SOME TRIGONOMETRIC SERIES', MATHEMATICS OF COMPUTATION, vol. 63, pp. 271 - 275, http://dx.doi.org/10.2307/2153573

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

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

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

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

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

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

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

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

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

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

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

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

McLean W;Mustapha K;Ali R;Knio O, 'Well-posedness and regularity of time-fractional, advection-diffusion-reaction equations', Well-posedness and regularity of time-fractional, advection-diffusion-reaction equations, http://arxiv.org/abs/1810.04836v1

Le KN;McLean W;Lamichhane B, 'Finite element approximation of a time-fractional diffusion problem in a non-convex polygonal domain', ANZIAM J. 59(2017), 61-82, http://dx.doi.org/10.1017/S1446181116000365


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