Abstract This paper reviews strong stability preserving discrete variable methods for differential systems. The Runge–Kutta have been usually investigated in the literature on subject, using so-called Shu–Osher representation of these methods, as a convex combination first-order steps by forward Euler method. In this paper, we revisit analysis reformulating subclass general linear ordinary equa...

High order splitting schemes with complex timesteps are applied to Kolmogorov backward equations stemming from stochastic differential equations in Stratonovich form. In the setting of weighted spaces, the necessary analyticity of the split semigroups can be easily proved. A numerical example from interest rate theory, the CIR2 model, is considered. The numerical results are robust for drift-do...

purpose : to compare results of different methods for true corneal power determination and intraocular lens (iol) power calculation formulas in 10 eyes of 7 patients with previous radial keratotomy (rk) with or without astigmatic keratotomy methods : in this case series study, we determined the corneal power of 10 eyes of 7 patients who had undergone rk with or without astigmatic keratotomy wit...

We derive a posteriori error estimates, which exhibit optimal global order, for a class of time stepping methods of any order that include Runge–Kutta Collocation (RK-C) methods and the continuous Galerkin (cG) method for linear and nonlinear stiff ODEs and parabolic PDEs. The key ingredients in deriving these bounds are appropriate one-degree higher continuous reconstructions of the approximat...

Phosphorylation of light-activated rhodopsin by the retina-specific enzyme, rhodopsin kinase (RK), is the primary event in the initiation of desensitization in the visual system. RK binds to the cytoplasmic face of rhodopsin, and the binding results in activation of the enzyme which then phosphorylates rhodopsin at several serine and threonine residues near the carboxyl terminus. To map the RK ...

The main purpose of the present work is multi-objective shape optimization of a projectile tip for impacting and normal penetrating. Velocity drop, weight and inner volume of projectile have been considered as three conflicting objective functions.  For this purpose, at the first step, finite element modeling was done using ABAQUS/Explicit and projectile penetration was examined in different ge...

An exponentially fitted explicit hybrid method for solving oscillatory problems is obtained. This method has four stages. The first three stages of the method integrate exactly differential systems whose solutions can be expressed as linear combinations of {1, x, exp μx , exp −μx }, μ ∈ C, while the last stage of this method integrates exactly systems whose solutions are linear combinations of ...