P. W. Sharp
University of Auckland
33 Papers
200 Citations
P. W. Sharp is an academic researcher from University of Auckland. The author has contributed to research in topics: Runge–Kutta methods & Initial value problem. The author has an hindex of 11, co-authored 33 publications. Previous affiliations of P. W. Sharp include University of Canterbury & University of Toronto.
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Papers
Self-similar solutions for elastohydrodynamic cavity flow
D. A. Spence,P. W. Sharp +1 more
TL;DR: In this paper, the enlargement of a lens-shaped cavity lying in a plane of cleavage between two elastic half spaces and filling with viscous fluid from a source on the axis of symmetry is considered.
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Buoyancy-driven crack propagation: a mechanism for magma migration
TL;DR: In this paper, a solution for steady propagation of a two-dimensional fluid fracture driven by buoyancy in an elastic medium is obtained for the vertical ascent of magma through the earth's mantle and crust.
179
Two-stage and Three-stage Diagonally Implicit Runge-Kutta Nyström Methods of Orders Three and Four
P. W. Sharp,J.M. Fine,K. Burrage +2 more
TL;DR: In this article, the existence of two-stage and three-stage R-stable, P-stable and RL-stable Runge-Kutta Nystrom methods with small principal truncation coefficients was investigated.
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Numerical comparisons of some explicit Runge-Kutta pairs of orders 4 through 8
TL;DR: Numerical testing of six explicit Runge-Kutta pairs showed how the performance could be alterednoticeably by making simple changes to the stepsize selection strategy, and new ways of presenting numericalcomparisons were demonstrated.
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N-body simulations: The performance of some integrators
TL;DR: It is found that the error growth on some integrations is noticeably slower than predicted by asymptotic analysis of the truncation and round-off error, suggesting that the numerical solutions near the end of a billion year simulation in double precision with variable-stepsize nonsymplectic methods would have poor accuracy.
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