In this paper a general class of diffusion problem is considered, where the standard time derivative is replaced by a fractional one. For the numerical solution, a mixed method is proposed, which consists of a finite difference scheme through space and a spectral collocation method through time. The spectral method considerably reduces the computational cost with respect to step-by-step methods to discretize the fractional derivative. Some classes of spectral bases are considered, which exhibit different convergence rates and some numerical results based on time diffusion reaction diffusion equations are given
The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and analyze a time integrator having the same property for all times. Furthermore, strong and weak convergence of the numerical scheme along with efficient multilevel Monte Carlo estimators are studied. Finally, extensive numerical experiments illustrate the performance of the proposed numerical scheme.
A new class of two-step Runge-Kutta methods for the numerical solution of ordinary differential equations is proposed. These methods are obtained using the collocation approach by relaxing some of the collocation conditions to obtain methods with desirable stability properties. Local error estimation for these methods is also discussed.
The aim of the present study was to evaluate the efficacy of an air purifier device (professional XXl inn-56 innoliving) with HEPA 14 filter in reducing the number of suspended particles generated during dental procedures as a vector of COVID-19 transmission. The survey was conducted on 80 individuals who underwent Oral Surgery with dental Hygiene Procedures, divided into two groups based on the operational risk classification related to dental procedures: a Test Group (with application of filtering device) and a Control Group (without filtering device). All procedures were monitored throughout the clinical controls, utilising professional tools such as molecular particle counters (Lasair III 350 L 9.50 L/min), bacteriological plates (Tryptic Soy Agar), sound meters for LAFp sound pressure level (SPL) and LCpk instantaneous peak level. The rate of suspended particles, microbiological pollution and noise pollution were calculated. SPSS software was used for statistical analysis method. The results showed the higher efficacy of the TEST Group on pollution abatement, 83% more than the Control fgroup. Additionally, the contamination was reduced by 69–80%. Noise pollution was not noticeable compared to the sounds already present in the clinical environment. The addition of PAC equipment to the already existing safety measures was found to be significantly effective in further microbiological risk reduction.
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