The modification presented here is one that leads to approximations that converge with high order rates of convergence with respect to domain size.
The reason for this is the switch to a spline time dependence with explicit damping of higher-order rates of change (∂ 2/∂ t 2 and ∂ 3/∂ t 3).
In addition, it preserves full accuracy, including higher-order rates of convergence, which we illustrate for boundary-fitted discretizations of several benchmark tests in one, two and three dimensions.
Questions that did not rate as higher order were revised and rated again until they earned a higher-order rating.
Griffith, C.S. Peskin, On the order of accuracy of the immersed boundary method: higher order convergence rates for sufficiently smooth problems, J. Comput.
We combine national data to update temporal trends and explore the effects of socioeconomic deprivation and maternal age on twin and higher order multiple maternity rates in England and associated stillbirth and neonatal mortality.
The highest first order rate constant, k value was 0.1172 h−1 with 97% Phe degradation; while the lowest k value was 0.0004 and phenanthrene was not degraded throughout the 7-d experiment.
The number of maternities by multiplicity of birth (singleton, twin, triplet and higher order) and the rate of multiple maternities were calculated by maternal age (5-year bands), deprivation decile and year of birth.
We provide a theorem which shows that we have arbitrarily high order convergence rates in terms of ε/η in the periodic setting.
This period has seen increasing rates of twin pregnancies and decreasing rates of higher order births which have coincided with changes in recommendations regarding assisted reproductive techniques.
For example, it is required that the system nonlinearities be known, or be bounded by known functions, or be linearly parametrized, or satisfy some high order growth rate condition, etc.
