By Associate Professor William McLean

Journal articles

Mustapha K; McLean W; Dick J, 2024, 'An α-Robust and Second-Order Accurate Scheme for a Subdiffusion Equation', Journal of Scientific Computing, 99, http://dx.doi.org/10.1007/s10915-024-02554-w

McLean W; Mustapha K, 2023, 'Error profile for discontinuous Galerkin time stepping of parabolic PDEs', Numerical Algorithms, 93, pp. 157 - 177, http://dx.doi.org/10.1007/s11075-022-01410-y

McLean W; Mustapha K, 2022, 'Uniform stability for a spatially discrete, subdiffusive Fokker–Planck equation', Numerical Algorithms, 89, pp. 1441 - 1463, http://dx.doi.org/10.1007/s11075-021-01160-3

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, 37, pp. 2429 - 2445, http://dx.doi.org/10.1002/num.22722

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, 85, pp. 82 - 83, http://dx.doi.org/10.1016/j.camwa.2021.01.008

McLean W, 2021, 'Numerical evaluation of Mittag-Leffler functions', Calcolo, 58, pp. 7, http://dx.doi.org/10.1007/s10092-021-00398-6

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, 30, pp. 567 - 601, http://dx.doi.org/10.4208/CICP.OA-2020-0124

McLean W, 2020, 'IMPLEMENTATION of HIGH-ORDER, DISCONTINUOUS GALERKIN TIME STEPPING for FRACTIONAL DIFFUSION PROBLEMS', ANZIAM Journal, 62, pp. 121 - 147, http://dx.doi.org/10.1017/S1446181120000152

McLean W; Mustapha K; Ali R; Knio OM, 2020, 'Regularity theory for time-fractional advection–diffusion–reaction equations', Computers and Mathematics with Applications, 79, pp. 947 - 961, http://dx.doi.org/10.1016/j.camwa.2019.08.008

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, 18, pp. 2765 - 2787, http://dx.doi.org/10.3934/cpaa.2019124

McLean W; Mustapha K; Ali R; Knio O, 2019, 'Well-posedness of time-fractional advection-diffusion-reaction equations', Fractional Calculus and Applied Analysis, 22, pp. 918 - 944, http://dx.doi.org/10.1515/fca-2019-0050

Liao HL; McLean W; Zhang J, 2019, 'A discrete Grönwall inequality with applications to numerical schemes for subdiffusion problems', SIAM Journal on Numerical Analysis, 57, pp. 218 - 237, http://dx.doi.org/10.1137/16M1175742

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, 40, pp. A3831 - A3852, http://dx.doi.org/10.1137/17M1125261

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, 59, pp. 61 - 61, http://dx.doi.org/10.21914/anziamj.v59i0.10940

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, 59, pp. 61 - 82, http://dx.doi.org/10.1017/S1446181116000365

Macnamara S; Henry B; McLean W, 2017, 'Fractional euler limits and their applications', SIAM Journal on Applied Mathematics, 77, pp. 447 - 469, http://dx.doi.org/10.1137/16M1091861

Le KN; McLean W; Mustapha K, 2016, 'Numerical solution of the time-fractional Fokker-Planck equation with general forcing', SIAM Journal on Numerical Analysis, 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, 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, 40, pp. 353 - 375, http://dx.doi.org/10.1007/s10444-013-9311-6

Wang K; McLean W; Kampwerth H; Wang K, 2013, 'Transient photoluminescence from silicon wafers: Finite element analysis', JOURNAL OF APPLIED PHYSICS, 114, http://dx.doi.org/10.1063/1.4826896

Kim IS; McLean W, 2013, 'Computing the hausdorff distance between two sets of parametric curves', Communications of the Korean Mathematical Society, 28, pp. 833 - 850, http://dx.doi.org/10.4134/CKMS.2013.28.4.833

Mustapha K; Mclean W, 2013, 'Superconvergence of a discontinuous Galerkin method for fractional diffusion and wave equations', SIAM Journal on Numerical Analysis, 51, pp. 491 - 515, http://dx.doi.org/10.1137/120880719

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, 53, pp. 134 - 134, http://dx.doi.org/10.21914/anziamj.v53i0.5248

Mclean W, 2012, 'Fast summation by interval clustering for an evolution equation with memory', SIAM Journal on Scientific Computing, 34, pp. A3039 - A3056, http://dx.doi.org/10.1137/120870505

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, 53, pp. 134 - 155, http://dx.doi.org/10.1017/S1446181112000107

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, 32, pp. 906 - 925, http://dx.doi.org/10.1093/imanum/drr027

McLean W, 2011, 'Regularity of solutions to a time-fractional diffusion equation', ANZIAM Journal, 52, pp. 123 - 138, http://dx.doi.org/10.1017/S1446181111000617

Le Gia QT; Mclean W, 2011, 'Numerical solution of a parabolic equation on the sphere using Laplace transforms and radial basis functions', ANZIAM Journal, pp. C89 - C102

Mclean W; Mustapha K, 2011, 'Piecewise-linear, discontinuous Galerkin method for a fractional diffusion equation', Numerical Algorithms, 56, pp. 159 - 184, http://dx.doi.org/10.1007/s11075-010-9379-8

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, 30, pp. 208 - 230, http://dx.doi.org/10.1093/imanum/drp004

Mclean W; Thomee V, 2010, 'Numerical solution via Laplace transforms of a fractional order evolution equation', Journal of Integral Equations and Applications, 22, pp. 57 - 94, http://dx.doi.org/10.1216/JIE-2010-22-1-57

Mustapha K; Mclean W, 2009, 'Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation', Numerical Algorithms, 52, pp. 69 - 88

Mustapha KA; Mclean W, 2009, 'Discontinuous galerkin method for an evolution equation with a memory term of positive type', Mathematics of Computation, 78, pp. 1975 - 1995

Mclean W; Mustapha K, 2007, 'A second-order accurate numerical method for a fractional wave equation', Numerische Mathematik, 105, pp. 481 - 510

Graham IG; Mclean W, 2006, 'Anisotropic mesh refinement: the conditioning of Galerkin boundary element matrices and simple preconditioners', SIAM Journal on Numerical Analysis, 44, pp. 1487 - 1513

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, 102, pp. 497 - 522

Mclean W; Thomee V, 2004, 'Time discretization of an evolution equation via Laplace transforms', IMA Journal of Numerical Analysis, 24, pp. 439 - 463

Jeon Y; Mclean W, 2003, 'A new boundary element method for the biharmonic equation with Dirichlet boundary conditions', Advances in Computational Mathematics, 19, pp. 339 - 365

Ainsworth M; Mclean W, 2003, 'Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes', Numerische Mathematik, 93, pp. 387 - 413

Ainsworth M; Mclean W; Tran T, 2000, 'Diagonal scaling of stiffness matrices in the Galerkin boundary element method', Journal of Australian Mathematical Society B, pp. 141 - 150

Mclean W; Steinbach O, 1999, 'Boundary element preconditioners for a hypersingular integral equation on an interval', Advances in Computational Mathematics, 11, pp. 271 - 286

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, pp. 1901 - 1932

Mclean W; Tran T, 1997, 'A preconditioning strategy of boundary element Galerkin methods', Numerical Methods for Partial Differential Equations, 13, pp. 283 - 301

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

Mclean W; Prossdorf S, 1996, 'Boundary element collocation methods using splines with multiple knots', Numerische Mathematik, pp. 419 - 451

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, pp. 49 - 69

Mclean W; Sloan IH, 1994, 'A fully discrete and symmetric boundary element method', IMA Journal of Numerical Analysis, 14, pp. 311 - 345, http://dx.doi.org/10.1093/imanum/14.3.311

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

McLean W, 1994, 'Fully-discrete collocation methods for an integral equation of the first kind', Journal of Integral Equations and Applications, 6, pp. 537 - 571, http://dx.doi.org/10.1216/jiea/1181075835

McLEAN W, 1994, 'Numerical evaluation of some trigonometric series', Mathematics of Computation, 63, pp. 271 - 274, http://dx.doi.org/10.1090/S0025-5718-1994-1240661-6

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