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pro vyhledávání: '"Macdonald, Colin B"'
The determination of the mean first passage time (MFPT) for a Brownian particle in a bounded 2-D domain containing small absorbing traps is a fundamental problem with biophysical applications. The average MFPT is the expected capture time assuming a
Externí odkaz:
http://arxiv.org/abs/2006.12722
We develop novel numerical methods and perturbation approaches to determine the mean first passage time (MFPT) for a Brownian particle to be captured by either small stationary or mobile traps inside a bounded 2-D confining domain. Of particular inte
Externí odkaz:
http://arxiv.org/abs/1911.07842
This article describes a reduction of a nonautonomous Brusselator reaction-diffusion system of partial differential equations on a spherical cap with time dependent curvature using the method of centre manifold reduction. Parameter values are chosen
Externí odkaz:
http://arxiv.org/abs/1810.04702
Akademický článek
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We demonstrate a method for filtering images defined on curved surfaces embedded in 3D. Applications are noise removal and the creation of artistic effects. Our approach relies on in-surface diffusion: we formulate Weickert's edge/coherence enhancing
Externí odkaz:
http://arxiv.org/abs/1403.2131
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 that adaptive stepsize control can be incorporated within a family of
Externí odkaz:
http://arxiv.org/abs/1310.6331
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 embedding method, which uses an implicit representation of the surface in
Externí odkaz:
http://arxiv.org/abs/1307.5657
Autor:
Chen, Yujia, Macdonald, Colin B.
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 equations on general curved surfaces. Based on the closest point representat
Externí odkaz:
http://arxiv.org/abs/1307.4354
Publikováno v:
SIAM J. Numer. Anal. 51-5 (2013), pp. 2887-2910
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 part of the spatial domain. Such methods may be convenient for problems
Externí odkaz:
http://arxiv.org/abs/1301.4006
Publikováno v:
SIAM J. Numer. Anal. 51-4 (2013), pp. 2149-2165
We apply the concept of effective order to strong stability preserving (SSP) explicit Runge-Kutta methods. Relative to classical Runge-Kutta methods, methods with an effective order of accuracy are designed to satisfy a relaxed set of order condition
Externí odkaz:
http://arxiv.org/abs/1207.2902