In this paper, we introduce the model of Bromsulphthalein (BSP) test whose components are BSP in blood, BSP in liver and BSP in bile with fractional order. Generalized Euler method (GEM) is performed to solve the problem. We compare fractional results and integer results with clinical data. The results show that the fractional order is closer than clinical data than standard model.

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We give an explicit error bound between the invariant density of an elliptic reflected diffusion in a smooth compact domain and the kernel estimator built on the symmetric Euler scheme introduced in Bossy, Gobet and Talay (2004).

It presents and analyzes the Euler methods for stochastic age-dependent population equations driven by Poisson random jump measure; Under the Local Lipschitz condition, we prove that the Euler approximation solution converges to the exact solution in the mean-square sense. An example is given to illustrates our results.

We use the elliptic reconstruction technique in combination with a duality approach to prove a posteriori error estimates for fully discrete backward Euler scheme for linear parabolic equations. As an application, we combine our result with the residual based estimators from the a posteriori estimation for elliptic problems to derive space-error estimators and thus a fully practical version of ...

We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may possibly be random. We introduce a new operator, the generalized infinitesimal generator, to obtain Taylor expansions of the asymptotic moments of the estimator...

In a previous paper it was shown that the Forward Euler method applied to differential inclusions where the right-hand side is a Lipschitz continuous set-valued function with uniformly bounded, compact values, converges with rate one. The convergence, which was there in the sense of reachable sets, is in this paper strengthened to the sense of convergence of solution paths. An improvement of th...

We use the elliptic reconstruction technique in combination with a duality approach to prove a posteriori error estimates for fully discrete backward Euler scheme for linear parabolic equations. As an application, we combine our result with the residual based estimators from the a posteriori estimation for elliptic problems to derive space-error indicators and thus a fully practical version of ...

Method: The presented EL method uses the open access software OpenFOAM to solve bubble dynamics with bubble interactions computed via Monte Carlo methods. The estimated bubble size distribution and the predicted hold-up are compared with experimental data and other simulative EE work with a reasonable consensus for both. Benchmarks with state of the art EE simulations shows that the EL approach...