87 citations · 270 across the 12 of their papers we have counts for
4 papers · 1 filter
Revisionist Integral Deferred Correction with Adaptive Stepsize Control
Andrew J. Christlieb, Colin B. Macdonald, Benjamin W. Ong +1
Adaptive stepsize control is a critical feature for the robust and efficient numerical solution of initial-value problems in ordinary differential equations. In this paper, we show…
An embedded method-of-lines approach to solving partial differential equations on surfaces
Ingrid von Glehn, Thomas März, Colin B. Macdonald
We introduce a method-of-lines formulation of the closest point method, a numerical technique for solving partial differential equations (PDEs) defined on surfaces. This is an embe…
The Closest Point Method and multigrid solvers for elliptic equations on surfaces
Yujia Chen, Colin B. Macdonald
Elliptic partial differential equations are important both from application and analysis points of views. In this paper we apply the Closest Point Method to solving elliptic equati…
Spatially partitioned embedded Runge-Kutta methods
David I. Ketcheson, Colin B. Macdonald, Steven J. Ruuth
We study spatially partitioned embedded Runge--Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different p…