ClinicalTrials.gov: NCT01095406 The worldwide increase in patient complexity, more concern for quality and safety, and a shortage of resources are the challenging terms of the equation many physicians and respiratory therapists have to face nowadays [ 1- 3].
The numerical solution of such equations is always challenging because of its strong nonlinear phenomena and strong discontinuous interfaces.
In many problems numerical solution of MHD equations is a challenging task due to the temporal stiffness of this system in the parameter regimes of interest.
Accurate prediction of interlaminar transverse stresses in smart piezolaminated structures through two-dimensional laminate theories that are efficient, directly from the constitutive equations, is a challenging task.
Since most fractional differential equations do not have exact and analytic solutions, the accurate numerical techniques for solving these fractional equations are a challenging and motivational research area in mathematics and engineering.
On the other hand, most of the important problems modeled by nonlinear degenerate partial differential equations are truly challenging and require further new approaches and techniques, and need our full attention and further efforts.
In this analysis, the diameter and height increment equations proved particularly challenging due to remeasurement data only being available for trees > 10 cm in DBH and a general lack of height remeasurement data, respectively.
The flash equations are particularly challenging to solve for non-ideal systems with many components, and many process simulators use some version of the inside-out algorithms (Boston and Britt, 1978) for performing such calculations.
In this paper we deal with the extension of the Fast Kinetic Scheme (FKS) (Dimarco and Loubère, 2013 [26]) originally constructed for solving the BGK equation, to the more challenging case of the Boltzmann equation.
Our numerical method is able to solve the governing equation even in the challenging case of limit cycle oscillators with a large number of state variables.
