1,822 research outputs found
The impact of a natural time change on the convergence of the Crank-Nicolson scheme
We first analyse the effect of a square root transformation to the time
variable on the convergence of the Crank-Nicolson scheme when applied to the
solution of the heat equation with Dirac delta function initial conditions. In
the original variables, the scheme is known to diverge as the time step is
reduced with the ratio of the time step to space step held constant and the
value of this ratio controls how fast the divergence occurs. After introducing
the square root of time variable we prove that the numerical scheme for the
transformed partial differential equation now always converges and that the
ratio of the time step to space step controls the order of convergence,
quadratic convergence being achieved for this ratio below a critical value.
Numerical results indicate that the time change used with an appropriate value
of this ratio also results in quadratic convergence for the calculation of the
price, delta and gamma for standard European and American options without the
need for Rannacher start-up steps
A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance
We present a simple and easy to implement method for the numerical solution
of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many
cases, the considered problems have only a viscosity solution, to which,
fortunately, many intuitive (e.g. finite difference based) discretisations can
be shown to converge. However, especially when using fully implicit time
stepping schemes with their desirable stability properties, one is still faced
with the considerable task of solving the resulting nonlinear discrete system.
In this paper, we introduce a penalty method which approximates the nonlinear
discrete system to first order in the penalty parameter, and we show that an
iterative scheme can be used to solve the penalised discrete problem in
finitely many steps. We include a number of examples from mathematical finance
for which the described approach yields a rigorous numerical scheme and present
numerical results.Comment: 18 Pages, 4 Figures. This updated version has a slightly more
detailed introduction. In the current form, the paper will appear in SIAM
Journal on Numerical Analysi
Coherence of a room-temperature CW GaAs/GaAlAs injection laser
The temporal coherence of a stripe-geometry double-heterojunction GaAs/GaAlAs laser operating CW at room temperature was determined. A heterodyne detection scheme was used involving the mixing of the laser field with a frequency-shifted and time-delayed image of itself in an interferometer. Because the laser device oscillated in several longitudinal modes, the autocorrelation function of its output exhibited resonances for specific time delays. The rate at which the amplitude of these resonances decreased with increasing time delays provided a measure of an apparent coherence length associated with individual longitudinal modes. The coherence length, so defined, was found to increase linearly with drive current in excess of threshold. This observation is interpreted as evidence that the intrinsic linewidth of a longitudinal mode is inversely proportional to the coherent optical power in that mode. Apparent coherence lengths were a few centimeters for a few milliwatts of total optical power emitted per facet. For a perfectly balanced interferometer, a sharp heterodyne beat signal was also observed when the laser device was operated considerably below threshold, i.e., in the LED mode
Recommended from our members
Invasive pulmonary aspergillosis complicating COVID-19 in the ICU - A case report.
It is not yet known, if critically ill COVID-19 patients are prone to fungal infections. We report a 69-year-old patient without typical risk factors for invasive pulmonary aspergillosis (IPA), who developed IPA two weeks after onset of symptoms. Our report shows that IPA may occur in critically ill COVID-19 patients
Evaluating Terrain for Harvesting Equipment Selection
A terrain evaluation model, utilizing a geographic information system, has been developed as a tool for planning large-scale industrial timber harvesting operations. The model combines terrain descriptions with machine operating criteria to produce maps delineating operable areas. The integration of the model with a harvest planning decision support system is discussed and an example is presented
Penalty Methods for the Solution of Discrete HJB Equations -- Continuous Control and Obstacle Problems
In this paper, we present a novel penalty approach for the numerical solution
of continuously controlled HJB equations and HJB obstacle problems. Our results
include estimates of the penalisation error for a class of penalty terms, and
we show that variations of Newton's method can be used to obtain globally
convergent iterative solvers for the penalised equations. Furthermore, we
discuss under what conditions local quadratic convergence of the iterative
solvers can be expected. We include numerical results demonstrating the
competitiveness of our methods.Comment: 31 Pages, 7 Figure
What are the triggers of Asian visitor satisfaction and loyalty in the Korean heritage site?
Based on complexity theory, this study examines a configurational model that uses motivation antecedents and demographic configurations to explore the causal recipes that lead to high and low levels of Asian visitor satisfaction and loyalty. Data were collected from 183 Chinese and Japanese visitors to the Hanok heritage site in Seoul, South Korea. Asymmetrical modeling using a fuzzy-set qualitative comparative analysis was applied and a combination of desired behavioral outcomes identified. Hanok experience from the motivation configuration and gender from the demographic configuration appeared as necessary conditions to make visitors satisfied and loyal. Key tenets of complexity theory are supported by the study's findings
The Cinchona Primary Amine-Catalyzed Asymmetric Epoxidation and Hydroperoxidation of α,β-Unsaturated Carbonyl Compounds with Hydrogen Peroxide
Using cinchona alkaloid-derived primary amines as catalysts and aqueous hydrogen peroxide as the oxidant, we have developed highly enantioselective Weitz–Scheffer-type epoxidation and hydroperoxidation reactions of α,β-unsaturated carbonyl compounds (up to 99.5:0.5 er). In this article, we present our full studies on this family of reactions, employing acyclic enones, 5–15-membered cyclic enones, and α-branched enals as substrates. In addition to an expanded scope, synthetic applications of the products are presented. We also report detailed mechanistic investigations of the catalytic intermediates, structure–activity relationships of the cinchona amine catalyst, and rationalization of the absolute stereoselectivity by NMR spectroscopic studies and DFT calculations
North American crayfish harbour diverse members of the Nudiviridae
Three novel crayfish-infecting nudiviruses from crayfish in North America represent the first genomic confirmation of nudiviruses in crayfish: Faxonius propinquus nudivirus (FpNV), Faxonius rusticus nudivirus (FrNV),and Faxonius virilis nudivirus (FvNV). Histopathology and electron microscopy revealed nuclear infections,including nuclear hypertrophy in hepatopancreatic epithelial cells and the presence of membrane-bound bacilliform virions. Metagenomic sequencing resulted in complete circular genome assembly, and phylogenetic analyses (based on nudivirus core genes) placed these viruses within the unofficial Epsilonnudivirus genus. One ofthe nudiviruses was detected in the antennal gland of its host, and another is correlated with invasive crayfishdecline in one infected lake ecosystem - suggesting a potential route for viral transmission through water, andpossible population level impact. This study highlights the importance of genomic and ecological data inelucidating the diversity and evolutionary relationships of the Nudiviridae, while expanding their known diversityand range of host species
- …