Numerical solution of parabolic Cauchy problems in planar corner domains

An iterative method for the parabolic Cauchy problem in planar domains having a finite number of corners is implemented based on boundary integral equations. At each iteration, mixed well-posed problems are solved for the same parabolic operator. The presence of corner points renders singularities of the solutions to these mixed problems, and this is handled with the use of weight functions together with, in the numerical implementation, mesh grading near the corners. The mixed problems are reformulated in terms of boundary integrals obtained via discretization of the time-derivative to obtain an elliptic system of partial differential equations. To numerically solve these integral equations a Nyström method with super-algebraic convergence order is employed. Numerical results are presented showing the feasibility of the proposed approach. © 2014 IMACS.

Medication errors in older people with mental health problems:a review

Objective - To review and summarise published data on medication errors in older people with mental health problems. Methods - A systematic review was conducted to identify studies that investigated medication errors in older people with mental health problems. MEDLINE, EMBASE, PHARMLINE, COCHRANE COLLABORATION and PsycINFO were searched electronically. Any studies identified were scrutinized for further references. The title, abstract or full text was systematically reviewed for relevance. Results - Data were extracted from eight studies. In total, information about 728 errors (459 administration, 248 prescribing, 7 dispensing, 12 transcribing, 2 unclassified) was available. The dataset related almost exclusively to inpatients, frequently involved non-psychotropics, and the majority of the errors were not serious. Conclusions - Due to methodology issues it was impossible to calculate overall error rates. Future research should concentrate on serious errors within community settings, and clarify potential risk factors.

The method of fundamental solutions for free surface Stefan problems

In this paper, free surface problems of Stefan-type for the parabolic heat equation are investigated using the method of fundamental solutions. The additional measurement necessary to determine the free surface could be a boundary temperature, a heat flux or an energy measurement. Both one- and two-phase flows are investigated. Numerical results are presented and discussed.

Uniqueness and counterexamples in some inverse source problems

Uniqueness of a solution is investigated for some inverse source problems arising in linear parabolic equations. We prove new uniqueness results formulated in Theorems 3.1 and 3.2. We also show optimality of the conditions under which uniqueness holds by explicitly constructing counterexamples, that is by constructing more than one solution in the case when the conditions for uniqueness are violated.