Research Publications (entered into Research Information Management System)

involving Mathematics

2011

Boglaev I , (2011) Monotone iterates with quadratic convergence rate for solving weighted average approximations to semilinear parabolic problems Applied Mathematics and Computation 217 6390-6400
McLachlan R , Sun Y , Tse P , (2011) Linear stability of partitioned Runge-Kutta methods SIAM Journal on Numerical Analysis 49 1 232-263
Modin K , Perlmutter M , Marsland S , McLachlan R , (2011) On Euler-Arnold equations and totally geodesic subgroups Journal of Geometry and Physics 61 8 1446-1461
Suebcharoen T , Van Brunt B , Wake G , (2011) Asymmetric cell division in a size-structured growth model Differential and Integral Equations 24 7-8 787-799
Wake G , Van Brunt B , (2011) A Mellin transform solution to a second-order pantograph equation with linear dispersion arising in a cell-growth model European Journal of Applied Mathematics 22 2 151-168

2010

(2010) Preservation and destruction of periodic orbits by symplectic integrators Numerical Algorithms 53 2-3 343-362
Boglaev I , (2010) Numerical solutions of coupled systems of nonlinear elliptic equations Numerical methods for partial differential equations online 1-20
Boglaev I , (2010) Monotone iterates for solving coupled systems of nonlinear parabolic equations Computing 92 1 65-95
Celledoni E , McLachlan R , Owren B , Quispel G , (2010) On conjugate B-series and their geometric study Journal of Numerical Analysis Industrial and Applied Mathematics 5 1-2 85-94
Elvin A , Laing C , McLachlan R , Roberts M , (2010) Exploiting the Hamiltonian structure of a neural field model Physica D: Nonlinear Phenomena 239 9 537-546
Hardy M , Boglaev I , (2010) Parallel monotone domain decomposition algorithms for nonlinear singularly perturbed reaction-diffusion problems of parabolic type Neural Parallel & Scientific Computations 18 253-268
McLachlan R , Celledoni E , Owren B , Quispel G , (2010) Energy-preserving integrators and the structure of B-series Foundations of Computational Mathematics 10 6 673-693

2009

(2009) Reconsidering Trigonometric Integrators The ANZIAM Journal 50 320-332
Hairer E, McLachlan RI, Skeel RD, (2009) On energy conservation of the simplified takahashi-Imada method Mathematical Modelling and Numerical Analysis 43 631-644
McLachlan RI, (2009) The structure of a set of vector fields on Poisson manifolds Journal of Physics A: Mathematical and Theoretical 42 142001-142003
McLachlan RI, Hairer E, Razakarivony A, (2009) Achieving Brouwer's Law with implicit Runge-Kutta methods BIT Numerical Mathematics 48 231-243
McLachlan RI, McLaren DI, Owren B, Celledoni E, Quispel GR, Wright WM, (2009) Energy-preserving runge-kutta Methods ESAIM:M2AN :Mathematical Modelling and Numerical Analysis 43 645-649
McLachlan RI, Quispel G, Tse PS, (2009) Linearization-preserving self-adjoint and symplectic integrators BIT Numerical Mathematics 49 177-197
McLachlan RI, Zhang X , (2009) Well-posedness of modified Camassa-Holm equations Journal of Differential Equations 246 3241-3259
Tuffley CP, (2009) Generalised knot groups distinguish the square and granny knots (with an appendix by David Savitt) Journal of Knot Theory and Its Ramifications 18 8 1129-1157

2008

Boglaev IP, (2008) Monotone iterates for solving systems of semilinear elliptic equations and applications Australian and New Zealand Industrial and Applied Mathematics Journal 49 591-608
Boglaev IP, Hardy M, (2008) A monotone domain decomposition algorithm for solving weighted average approximations to nonlinear singularly perturbed parabolic problems. Journal of Computational Mathematics 26 1 76-97
Boglaev IP, Pack S, (2008) Block mnotone domain decomposition methods for a quasi-linear anisotropic convection-diffusion equation Australian and New Zealand Industrial and Applied Mathematics Journal 49 493-512
Boglaev IP, Pack S, (2008) A uniformly convergent method on arbitrary meshes for a semilinear convection-diffusion problem with discontinuous data International Journal of Numerical Analysis and Modeling 5 1 24-39
de Carvalho MH, Little CH, (2008) Vector spaces and the Petersen graph The Electronic Journal of Combinatorics 15 1, R9 unpaged--
McLachlan RI, (2008) Explicit volume-preserving splitting methods for linear and quadratic divergency-free vector fields Foundations of Computational Mathematics 8 335-355
Ryland BN, McLachlan RI, (2008) On multisymplecticity of partitioned Runge-Kutta methods SIAM Journal on Scientific Computing 30 3 1318-1340

2007

Bernstein M, Tuffley CP, (2007) Level structures on the Weierstrass family of cubics Communications in Algebra 35 4 1249-1261
Boglaev IP, (2007) On a block monotone domain decomposition algorithm for a nonlinear reaction-diffusion problem Journal of Computational Analysis and Applications 9 1 55-75
Boglaev IP, (2007) The solution of a semilinear evolutionary convection-diffusion problem by a monotone domain decomposition algorithm Applied Mathematics and Computation 197 536-547
Boglaev IP, Hardy M, (2007) Uniform convergence of a weighted average scheme for a nonlinear reaction-diffusion problem Journal of Computational and Applied Mathematics 200 2 705-721
McLachlan RI, (2007) A new implementation of sympletic Runge-Kutta methods SIAM Journal on Scientific Computing 29 4 1637-1649
McLachlan RI, Marsland SR, (2007) Discrete mechanics and optimal control for image registration ANZIAM Journal 48 1-16
McLachlan RI, Marsland SR, (2007) N-particle dynamics of the Euler equations for planar diffeomorphisms Dynamical Systems 22 3 269-290
McLachlan RI, Marsland SR, (2007) Discrete mechanics and optimal control for image registration Australian and New Zealand Industrial and Applied Mathematics Journal 48 C1-C16
Pack S, Boglaev IP, (2007) Parallel two-level Schwarz algorithm for solving singularly perturbed convection-diffusion problems 43rd Applied Mathematics Conference (ANZIAM 2007)
Perlmutter MJ, Rodriguez-Olmos M, Sousa-Dias ME, (2007) On the geometry of reduced cotangent bundles at zero momentum Journal of Geometry and Physics 57 2 571-596
Ryland BN, McLachlan RI, Frank J, (2007) On the multisymplecticity of partitioned Runge-Kutta and splitting methods International Journal of Computer Mathematics 84 6 847-869
Tuffley CP, (2007) Popping bubbles Notices of the American Mathematical Society 54 6 746-747
Van Brunt B, Vlieg-Hulstman M, (2007) Evolution equations having conservation laws with flux characteristics ANZIAM Journal 29 1 39-52

2006

Boglaev IP, (2006) A block monotone domain decomposition algorithm for a nonlinear singularly perturbed parabolic problem International Journal of Numerical Analysis and Modeling 3 2 211-231
Boglaev IP, (2006) Monotone iterates for solving nonlinear monotone difference schemes Computing 78 1 17-30
Boglaev IP, (2006) Domain decomposition for a parabolic convection-diffusion problem Numerical Methods for Partial Differential Equations 22 6 1361-1378
Boglaev IP, (2006) Monotone algorithms for solving nonlinear monotone difference schemes of parabolic type in the canonical form Journal of Numerical Mathematics 14 4 247-266
Boglaev IP, (2006) Monotone iterates for nonlinear difference schemes of parabolic type in the canonical form 13th Biennial Computational Techniques and Applications Conference
Boglaev IP, (2006) Monotone iterates for solving coupled systems of nonlinear elliptic equations New Zealand Mathematics Colloquium
Boglaev IP, Hardy M, (2006) Monotone finite difference domain decomposition algorithms and applications to nonlinear singularly perturbed reaction-diffusion problems Advances in Difference Equations 2006 Article ID 70325 1-38
Boglaev IP, Pack S, (2006) A uniformly convergent method for a singularly perturbed semilinear reaction-diffusion problem with discontinuous data Applied Mathematics and Computation 182 1 244-257
Little CH, Vince A, (2006) Parity versions of 2-connectedness Electronic Journal of Combinatorics 13 1-14
Mason IG, McLachlan RI, Gerard DT, (2006) A double exponential model for biochemical oxygen demand Bioresource Technology 97 2 273-282
McLachlan RI, (2006) Geometric integration for a two-spin system Journal of Physics A: Mathematical and General 39 27 L447-L452
McLachlan RI, Marsland SR, (2006) The Kelvin-Helmholtz instability of momentum sheets in the Euler equations for planar diffeomorphisms Journal on Applied Dynamical Systems 5 4 726-758
McLachlan RI, Perlmutter MJ, (2006) Integrators for nonholonomic mechanical systems Journal of Nonlinear Science 16 4 283-328
McLachlan RI, Quispel GR, (2006) Geometric numerical integration of differential equations Journal of Physics A: Mathematical and General 39 19 1-3
McLachlan RI, Quispel GR, (2006) Geometric integrators for ODEs Journal of Physics A: Mathematical and General 39 19 5251-5285
Rynhart PR, Boglaev IP, (2006) Parallel monotone domain decomposition algorithms for solving nonlinear reaction-diffusion problems with mixed boundary conditions 42nd Applied Mathematics Conference 55-

2005

Ascher UM, McLachlan RI, (2005) On symplectic and multisymplectic schemes for the KdV equation Journal of Scientific Computing 25 1 83-104
Boglaev IP, (2005) A block monotone domain decomposition algorithm for a semilinear convection-diffusion problem Journal of Computational and Applied Mathematics 173 259-277
Boglaev IP, (2005) Schwarz alternating algorithms for a convection-diffusion problem Journal of Applied Mathematics and Computations 165 647-668
Boglaev IP, (2005) Uniform convergence of monotone iterative methods for semilinear singularly perturbed problems of elliptic and parabolic types Electronic Transactions on Numerical Analysis 20 86-103
Boglaev IP, (2005) Monotone Schwarz iterates for a semilinear parabolic convection-diffusion problem Journal of Computational and Applied Mathematics 183 191-209
Boglaev IP, (2005) A monotone weighted average method for non-linear reaction-diffusion problem International Journal of Computer Mathematics 82 8 1017-1031
Hardy MP, Boglaev IP, (2005) Parallel implementation of a monotone domain decomposition algorithm for nonlinear reaction-diffusion problems ANZIAM Journal 46 290-303
Hartmann S, Little CH, (2005) Even bonds of prescribed directed parity The Electronic Journal of Combinatorics 12 1 1-15
Mason IG, McLachlan RI, Gerard DT, (2005) A double exponential model for biochemical oxygen demand Bioresource Technology 97 273-282

2004

Ascher UM, McLachlan RI, (2004) Multisymplectic box schemes and the Korteweg-de Vries equation Applied Numerical Mathematics 48 255-269
Basse B, Baguley BC, Marshall ES, Joseph WR, Van Brunt B, Wake GC, Wall DJ, (2004) Modelling cell death in human tumour cell lines exposed to the anticancer drug paclitaxel Journal of Mathematical Biology 49 329-357
Boglaev IP, (2004) Monotone iterative algorithms for a nonlinear singularly perturbed parabolic problem Journal of Computational and Applied Mathematics 172 313-335
Boglaev IP, (2004) Uniform numerical methods on arbitrary meshes for singularly perturbed problems with discontinuous data Applied Mathematics and Computation 154 815-833
Boglaev IP, (2004) A monotone Schwarz algorithm for a semilinear convection-diffusion problem Journal of Numerical Mathematics 12 3 169-191
Boglaev IP, (2004) On monotone iterative methods for a nonlinear singularly perturbed reaction-diffusion problem Journal of Computational and Applied Mathematics 162 445-466
Boglaev IP, (2004) Physically motivated domain decomposition for singularly perturbed equations
Boglaev IP, Duoba V, (2004) Iterative domain decomposition algorithms for a convection-diffusion problem Computers and Mathematics with Applications 47 501-518
Boglaev IP, Duoba V, (2004) On an uniform multidomain decomposition method applied to a singularly perturbed problem with regular boundary layers Journal of Computational and Applied Mathematics 166 13-29
Boglaev IP, Hardy MP, (2004) Parallel implementation of a domain decomposition algorithm for nonlinear reactions: Diffusion problems
Dong FM, Hendy MD, Teo K, Little CH, (2004) Graph-functions associated with an edge-property Australasian Journal of Combinatorics 30 3-20
Dong FM, Hendy MD, Teo K, Little CH, Koh KM, (2004) Chromatically unique multibridge graphs Electronic Journal of Combinatorics 11 1 1-11
Kathirgamanathan P, McKibbin R, McLachlan RI, (2004) Source release-rate estimation of atmospheric pollution from a non-steady point source at a known location Environmental Modeling and Assessment 9 33-42
Little CH, Teo K, Norine S, (2004) A new proof of a characterisation of Pfaffian bipartite graphs Journal of Combinatorial Theory. Series B 91 1 123-126
McLachlan RI, (2004) [Untitled] Newsletter of the New Zealand Mathematical Society 90 49-50
McLachlan RI, Perlmutter MJ, (2004) Energy drift in reversible time integration Journal of Physics A: Mathematical and General 37 L593-L598
McLachlan RI, Perlmutter MJ, (2004) Energy drift in reversible time integration Journal of Physics A: Mathematical and General 37 45 L593-L598
McLachlan RI, Perlmutter MJ, Quispel GR, (2004) On the nonlinear stability of symplectic integrators BIT Numerical Mathematics 44 99-117
McLachlan RI, Quispel GR, (2004) Explicit geometric integration of polynomial vector fields BIT Numerical Mathematics 44 515-538
McLachlan RI, Zanna A, (2004) The discrete Moser-Veselov algorithm for the free rigid body, revisited The Journal of the Society for the Foundations of Computational Mathematics 5 87-123
Van Brunt B, Basse B, Wake GC, Wall DJ, (2004) On a cell-growth model for plankton Mathematical Medicine and Biology 21 49-61
Van Brunt B, Marshall JC, Wake GC, (2004) Holomorphic solutions to pantograph type equations with neutral fixed points Journal of Mathematical Analysis and Applications 295 557-569
Vlieg M, Van Brunt B, Pidgeon D, Halford WD, (2004) Conservation laws for second-order parabolic partial differential equations ANZIAM Journal 45 333-348

2003

Boglaev IP, Duoba V, (2003) Domain decomposition for an advection-diffusion problem with parabolic layers Applied Mathematics and Computation 146 27-53
Fischer I, Little CH, (2003) Even circuits of prescribed clockwise parity The Electronic Journal of Combinatorics 10 1-20
Gascuel O , Hendy D , Jean-marie A , McLachlan RI, (2003) The combinatorics of tandem duplication trees Systematic Biology 52 1 110-118
Kathirgamanathan P, McKibbin R, McLachlan RI, (2003) Source release-rate estimation of atmospheric pollution from a non-steady point source - Part 1: Source at a known location Research Letters in Informational and Mathematical Sciences 5 71-84
Kathirgamanathan P, McKibbin R, McLachlan RI, (2003) Source release-rate estimation of atmospheric pollution from a non-steady point source - Part 2: Source at an unknown location Research Letters in Information and Mathematical Sciences 5 85-118
Kitson A, McLachlan RI, Robidoux N, (2003) Skew-adjoint finite difference methods on nonuniform grids New Zealand Journal of Mathematics 32 139-159
Little CH, Teo K, Van Brunt B, (2003) The number systems of analysis pp
Marshall JC, Wake GC, Van Brunt B, (2003) An eigenvalue problem for holomorphic solutions to a certain class of functional differential equations European Journal of Applied Mathematics 14 571-585
McLachlan RI, (2003) [Untitled] New Zealand Mathematical Society Newsletter 87 34-35
McLachlan RI, (2003) [Untitled] Society for Industrial and Applied Mathematics Review 45 4 817-821
McLachlan RI, (2003) Spatial discretization of partial differential equations with integrals IMA Journal of Numerical Analysis 23 4 645-664
McLachlan RI, Perlmutter MJ, Quispel GR, (2003) Lie group foliations: Dynamical systems and integrators Future Generation Computer Systems 19 1207-1219
McLachlan RI, Quispel GR, (2003) Geometric integration of conservative polynomial ODEs Applied Numerical Mathematics 45 4 411-418
McLachlan RI, Ryland BN, (2003) The algebraic entropy of classical mechanics Journal of Mathematical Physics 44 7 3071-3087
Rapson GL, Li X, Flenley JR, McLachlan RI, (2003) Testing vegetation dynamics around sponge swamp and Tiniroto Lakes: A numerical analysis
Rynhart PR, Jones JR, McLachlan RI, McKibbin R, (2003) Solution of the Young-Laplace equation for three particles CHEMECA 2003: 31st Australasian Chemical Engineering Conference: Proceedings unpaged-
Rynhart PR, McLachlan RI, Jones JR, McKibbin R, (2003) Solution of the Young-Laplace equation for three particles Research Letters in the Information and Mathematical Sciences 5 119-127
Rynhart PR, McLachlan RI, McKibbin R, (2003) Liquid bridges between three particles
Van Brunt B, Basse B, Baguley BC, Marshall ES, Joseph WR, Wake GC, Wall DJ, (2003) A mathematical model for analysis of the cell cycle in cell lines derived from human tumors Journal of Mathematical Biology 47 4 295-312

2002

Boglaev IP, (2002) The solution of a singularly perturbed convection-diffusion problem by an iterative domain decomposition method Numerical Algorithms 31 27-46
Boglaev IP, (2002) Uniform convergent methods on arbitrary meshes for singularly perturbed problems with piecewise smooth coefficients Research Letters in Information and Mathematical Sciences 3 1-
Boglaev IP, Duoba V, (2002) Uniform domain decomposition for a singularly perturbed problem with regular layers International Conference on Boundary and Interior Layers, Computational and Asymptotic Methods 49-54
Jones JR, Rynhart PR, McKibbin R, McLachlan RI, (2002) Mathematical modelling of granulation: Static and dynamic liquid bridges 4th World Congress on Particle Technology: Proceedings unpaged-
Little CH, Fischer I, Rendl F, (2002) Towards a characterisation of Pfaffian near bipartite graphs Discrete Mathematics 244 279-297
McKibbin R, Kathirgamanathan P, McLachlan RI, (2002) Source term estimation of pollution from an instantaneous point source Research Letters in the Information and Mathematical Sciences 3 59-67
McLachlan RI, (2002) Splitting methods Acta Numerica 341-434
McLachlan RI, (2002) The emerging science of geometric integration New Zealand Science Review 59 3&4 114-115
McLachlan RI, (2002) Families of high-order composition methods Numerical Algorithms 31 31 233-246
Rynhart PR, McKibbin R, McLachlan RI, Jones JR, (2002) Mathematical modelling of granulation: Static and dynamic liquid bridges Research Letters in the Information and Mathematical Sciences 3 1 199-212
Teo K, Dong FM, Hendy MD, Little CH, (2002) Zeros of adjoint polynomials of paths and cycles Australasian Journal of Combinatorics 25 167-174
Teo K, Dong FM, Koh KM, Hendy MD, (2002) Non-chordal graphs having integer-root chromatic polynomials II Discrete Mathematics 245 247-253
Teo K, Dong FM, Little CH, Hendy MD, (2002) Chromaticity of some families of dense graphs Discrete Mathematics 258 303-321
Teo K, Dong FM, Little CH, Hendy MD, (2002) Two invariants for adjointly equivalent graphs Australasian Journal of Combinatorics 25 133-143
Teo K, Koh KM, Dong FM, (2002) A note on the chromaticity of some 2-connected (n,n+3)-graphs Discrete Mathematics 243 217-221
Teo K, Little CH, Dong FM, Hendy MD, (2002) The vertex-cover polynomial of a graph Discrete Mathematics 250 71-78
Van Brunt B, Marshall JC, Wake GC, (2002) Natural boundaries for solutions to a certain class of functional differential equations Journal of Mathematical Analysis and Applications 268 157-170

2001

Boglaev IP, (2001) Domain decomposition for a singularly perturbed parabolic problem with a convection-dominated term Journal of Computational and Applied Mathematics 134 283-299
Boglaev IP, Duoba V, (2001) Domain decomposition for a singularly perturbed problem with parabolic layers Topics in Applied and Theoretical Mathematics and Computer Science 12 pp
Hendy MD, Dong FM, Koh KM, Teo K, Little CH, (2001) Sharp bounds for the number of 3-independent partitions and the chromaticity of bipartite graphs Journal of Graph Theory 37 48-77
Kim H, Van Brunt B, Wake GC, (2001) On a singular Sturm-Liouville problem involving an advanced functional differential equation European Journal of Applied Mathematics 12 625-644
Little CH, Fischer I, (2001) A characterisation of Pfaffian near Bipartite graphs Journal of Combinatorial Theory 82 175-222
McLachlan RI, (2001) [Untitled] New Zealand Mathematical Society Newsletter 83 23
McLachlan RI, McKibbin R, Kathirgamanthan P, (2001) Source term estimation of pollution from an instantaneous point source MODSIM 2001, International Congress on Modelling and Simulation Part 2 1013-1018
McLachlan RI, Perlmutter MJ, (2001) Conformal Hamiltonian systems Journal of Geometry and Physics 39 276-300
McLachlan RI, Quispel GR, (2001) What kinds of dynamics are there? Lie pseudogroups, dynamical systems, and geometric integration Nonlinearity 14 6 1689-1705
Quispel GR, McLachlan RI, (2001) Six Lectures on Geometric Integration of ODEs Foundations of Computational Mathematics 284 210 pp
Teo K, Dong FM, Koh KM, (2001) Structures and chromaticity of extremal 3-colourable sparse graphs Graphs and Combinatorics 17 4 611-635
Teo K, Dong FM, Little CH, Hendy MD, (2001) Some inequalities on chromatic polynomials New Zealand Journal of Mathematics 30 111-118
Van Brunt B, Vlieg M, Halford WD, Selvaratnam AR, (2001) On the solution of a class of second order quasi-linear PDEs and the Gauss equation ANZIAM Journal 42 312-323
Van Brunt B, Wiles P, (2001) Optimal location of transshipment depots Transport Research Part A 35 745-771

2000

Boglaev IP, (2000) Domain decomposition in boundary layers for singularly perturbed problems Applied Numerical Mathematics 34 (2000) 145-166
Boglaev IP, (2000) Numerical methods for singular perturbation problems and their parallel implementation 16th Institute for Mathematics and Computer Science World Congress 312-313
Cooper S, Kim H, Wake GC, Van Brunt B, (2000) Functional differential equations for cell-growth models with dispersion Communications in Applied Analysis 4 4 561-573
Little CH, Campbell AE, (2000) Evolutionary Families of Sets Electronic Journal of Combinatorics 7 unpaged-
Little CH, Dong FM, Koh KM, Teo K, Hendy MD, (2000) Chromatically unique bipartite graphs with low 3-independent partition numbers Discrete Mathematics 224 107-124
Marsden JE, Perlmutter MJ, (2000) The orbit bundle picture of cotangent bundle reduction Mathematical Reports of the Academy of Sciences, The Royal Society of Canada (C. R. Math. Rep. Acad. Sci. Canada) 22 2 33-55
McLachlan RI, Quispel GR, (2000) Numerical integrators that contract volume Applied Numerical Mathematics 34 253-260

Contact IFS | Contact Massey | About Massey | Massey Sitemap | Disclaimer