In this paper, we study the consistency of a variant of fractionalstep Runge–Kutta methods. These methods are designed tointegrate efficiently semi-linear multidimensional parabolicproblems by means of linearly implicit time integration processes.Such time discretization procedures are also related to a splittingof the space differential operator (or the spatial discretizationof it) as a sum of ‘simpler’ linear differentialoperators and a nonlinear term. 相似文献
In this study, the surfaces of ultrahigh molecular weight polyethylene (UHMWPE), poly(ethylene terephthalate) (PET), and polytetrafluoroethylene (PTFE) films were treated with a helium‐water vapor plasma at atmospheric pressure and room temperature. Surface changes related to hydrophilicity, chemical funtionalization, surface energy, and adhesive strength after plasma treatment were investigated using water contact angle (WCA) measurements, X‐ray photoelectron spectroscopy (XPS), and mechanical T‐peel tests. Results indicate increased surface energy accompanied with enhanced hydrophilicity. WCA decreased by 36, 50, and 16% for UHMWPE, PET, and PTFE, respectively, after only 0.4 s treatment. For UHMWPE, it is shown that the surface functionalization can be tailored depending on the plasma exposure time. Aging studies performed for these three polymers show the stability of the surface groups as indicated by a small increase in WCA values of plasma treated samples which can be attributed to cross‐linking of surface and subsurface polymer chains. XPS analysis of the surfaces show increased oxygen content via the formation of polar, hydroxyl‐based functional groups. Furthermore, major changes in the polymer structure of PET are observed, possibly due to the opening of the aromatic rings caused by the plasma energetic species. T‐peel test results show an 8, 7.5, and 400‐fold increase in peel strength for UHMWPE, PET, and PTFE, respectively. Most importantly, it is shown that water‐vapor based plasmas can be a promising, “green,” inexpensive route to promote the surface activation of polymers.
In this work we design and analyze an efficient numerical method to solve two dimensional initial-boundary value reaction–diffusion
problems, for which the diffusion parameter can be very small with respect to the reaction term. The method is defined by
combining the Peaceman and Rachford alternating direction method to discretize in time, together with a HODIE finite difference
scheme constructed on a tailored mesh. We prove that the resulting scheme is ε-uniformly convergent of second order in time
and of third order in spatial variables. Some numerical examples illustrate the efficiency of the method and the orders of
uniform convergence proved theoretically. We also show that it is easy to avoid the well-known order reduction phenomenon,
which is usually produced in the time integration process when the boundary conditions are time dependent.
This research has been partially supported by the project MEC/FEDER MTM2004-01905 and the Diputación General de Aragón. 相似文献
