By Associate Professor William McLean

Books

Mclean W, 2000, Strongly elliptic systems and boundary integral equations, Cambridge University Press, UK

Book Chapters

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

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

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

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

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

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