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In this paper a singularly perturbed reaction-diffusion partial differential equation in two space dimensions is examined. By means of an appropriate decomposition, we describe the asymptotic behaviour of the solution of problems of this kind. A central finite difference scheme is constructed for this problem which involves an appropriate Shishkin mesh. We(More)
The genesis of cardiogenic oscillations, i.e. the small waves in airway pressure (COS(paw)) and flow (COS(flow)) signals recorded at the airway opening is under debate. We hypothesized that these waves are originated from cyclic changes in pulmonary artery (PA) pressure and flow but not from the physical transmission of heartbeats onto the lungs. The aim of(More)
SUMMARY In this paper we present efficient multigrid methods for systems of partial differential equations that are governed by a dominating grad-div operator. In particular, we show that distributive smoothing methods give multigrid convergence factors that are independent of problem parameters and of the mesh sizes in space and time. The applications(More)
Keywords: Parabolic reaction–diffusion problems Semidiscrete problems Asymptotic behavior Uniform convergence Special nonuniform mesh a b s t r a c t In this work we are interested in the numerical approximation of 1D parabolic singularly perturbed problems of reaction–diffusion type. To approximate the multiscale solution of this problem we use a numerical(More)
Keywords: Parabolic reaction–diffusion problems Hybrid method Uniform convergence High order Vulanovic´mesh a b s t r a c t This paper deals with the numerical approximation of the solution of 1D parabolic singularly perturbed problems of reaction–diffusion type. The numerical method combines the standard implicit Euler method on a uniform mesh to(More)