Australian Mathematical Society (AustMS): E-Journals
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Solvability of a system of polynomial equations modulo primes
No full texthttp://dx.doi.org/10.1017/S0004972712000330
A comprehensive study of option pricing with transaction costs
No full text http://dx.doi.org/10.1017/S000497271200033
Statistical stability for deterministic and random dynamical systems
No full texthttp://dx.doi.org/10.1017/S000497271200033
A preconditioning-based analysis for a Bakhvalov-type mesh
Get PDFA new preconditioning-based parameter-uniform convergence analysis is presented for one-dimensional singularly perturbed convection-diffusion problems discretized by an upwind difference scheme on a Bakhvalov-type mesh. The proof technique utilizes the classical convergence principle: uniform stability and uniform consistency imply uniform convergence, which can only be used after applying an appropriate preconditioner to the discrete operator.
References
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I. P. Boglaev. Approximate solution of a non-linear boundary value problem with a small parameter for the highest-order differential. USSR Comput. Math. Math. Phys. 24.6 (1984), pp. 30–35. doi: 10.1016/0041-5553(84)90005-3.
T. Linß. Layer-adapted meshes for reaction-convection-diffusion problems. Vol. 1985. Lecture Notes in Mathematics. Springer-Verlag, 2010. doi: 10.1007/978-3-642-05134-0.
T. Linß, H.-G. Roos, and R. Vulanović. Uniform pointwise convergence on Shishkin-type meshes for quasi-linear convection-diffusion problems. SIAM J. Numer. Anal. 38.3 (2000), pp. 897–912. doi: 10.1137/S0036142999355957.
V. D. Liseikin. Layer resolving grids and transformations for singular perturbation problems. De Gruyter, 2001. doi: 10.1515/9783110941944.
T. A. Nhan, M. Stynes, and R. Vulanović. Optimal uniform-convergence results for convection-diffusion problems in one dimension using preconditioning. J. Comput. Appl. Math. 338 (2018), pp. 227–238. doi: 10.1016/j.cam.2018.02.012.
T. A. Nhan and R. Vulanović. Analysis of the truncation error and barrier-function technique for a Bakhvalov-type mesh. Electron. Trans. Numer. Anal. 51 (2019), pp. 315–330. doi: 10.1553/etna_vol51s315
T. A. Nhan and R. Vulanović. The Bakhvalov mesh: a complete finite-difference analysis of two-dimensional singularly perturbed convection-diffusion problems. Numer. Alg. 87 (2021), pp. 203–221. doi: 10.1007/s11075-020-00964-z
H.-G. Roos and T. Linß. Sufficient conditions for uniform convergence on layer-adapted grids. Computing 63.1 (1999), pp. 27–45. doi: 10.1007/s006070050049.
H.-G. Roos and M. Stynes. Some open questions in the numerical analysis of singularly perturbed differential equations. Comput. Meth. Appl. Math. 15.4 (2015), pp. 531–550. doi: 10.1515/cmam-2015-0011.
H.-G. Roos, M. Stynes, and L. Tobiska. Robust numerical methods for singularly perturbed differential equations. Vol. 24. Springer Series in Computational Mathematics. Springer-Verlag, 2008. doi: 10.1007/978-3-540-34467-4
G. I. Shishkin. A difference scheme for a singularly perturbed equation of parabolic type with discontinuous boundary conditions. USSR Comput. Math. Math. Phys. 28.6 (1988), pp. 32–41. doi: 10.1016/0041-5553(88)90039-0.
M. Stynes. Steady-state convection-diffusion problems. Acta Numer. 14 (2005), pp. 445–508. doi: 10.1017/S0962492904000261.
R. Vulanović and T. A. Nhan. Robust hybrid schemes of higher order for singularly perturbed convection-diffusion problems. Appl. Math. Comput. 386 (2020), p. 125495. doi: 10.1016/j.amc.2020.125495.
R. Vulanović and T. A. Nhan. Uniform convergence via preconditioning. Int. J. Numer. Anal. Model. Ser. B 5.4 (2014), pp. 347–356. url: www.global-sci.org/intro/article_detail/ijnamb/239.htm
MISG, mines and variability
Get PDFIn 2016, a Mathematics-in-Industry Study Group (MISG) project considered the construction of mining sequences, that is, the process connecting ore extraction with specific orders. In particular, the meeting considered the potential for using knowledge about geological variability within the ore. This article revisits this MISG project and the approach developed for thinking about the problem as the build for an order progresses. We provide new perspectives on this approach and outline possible ways for further development.
References
L. Caccetta and S. P. Hill. An application of branch and cut to open pit mine scheduling. J. Global Opt. 27 (2003), pp. 349–365. doi: 10.1023/A:1024835022186
M. Ibrahimov, A. Mohais, S. Schellenberg, and Z. Michalewicz. Scheduling in iron ore open-pit mining. Int. J. Adv. Man. Tech. 72.5–8 (2014), pp. 1021–1037. doi: 10.1007/s00170-014-5619-8
M. Menabde, G. Froyland, P. Stone, and G. A. Yeates. Mining schedule optimisation for conditionally simulated orebodies. Advances in Applied Strategic Mine Planning. Ed. by R. Dimitrakopoulos. Springer International Publishing, 2018, pp. 91–100. doi: 10.1007/978-3-319-69320-0_8
W. L. Sweatman, K. White, A. Albrecht, M. Peron, P. Pudney, and D. Whittle. Mining sequencing to control blend quality. Proceedings of the 2016 Mathematics and Statistics in Industry Study Group, MISG-2016. Ed. by P. Pudney and A. J. Roberts. Vol. 58. ANZIAM J. 2018, pp. M33–M66. doi: 10.21914/anziamj.v58i0.1247
A family of -supercongruences modulo the cube of a cyclotomic polynomial
No full texthttp://dx.doi.org/10.1017/S000497271200033
Electrical impedance tomography using nonconforming mesh and posterior approximated regression
No full texthttp://dx.doi.org/10.1017/S000497271200033