scholarly journals A Green’s function-based iterative approach to the pricing of American options

2008 ◽  
Author(s):  
M. Y. Melnikov
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
American Options ◽  
Iterative Approach

Green’s Function Iterative Approach for Solving Strongly Nonlinear Oscillators

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Marwan Abukhaled
Keyword(s):  
Fixed Point ◽  
Green’S Function ◽  
Green's Function ◽  
Nonlinear Oscillators ◽  
Iterative Approach ◽  
Numerical Examples ◽  
Strongly Nonlinear ◽  
Homotopy Perturbation ◽  
Linear Integral ◽  
Strongly Nonlinear Oscillators

In this paper, a Green’s function based iterative algorithm is proposed to solve strong nonlinear oscillators. The method’s essential part is based on finding an appropriate Green’s function that will be incorporated into a linear integral operator. An application of fixed point iteration schemes such as Picard’s or Mann’s will generate an iterative formula that gives reliable approximations to the true periodic solutions that characterize these kinds of equations. The applicability and stability of the method will be tested through numerical examples. Since exact solutions to these equations usually do not exist, the proposed method will be tested against other popular numerical methods such as the modified homotopy perturbation, the modified differential transformation, and the fourth-order Runge–Kutta methods.

GREEN'S FUNCTION MATCHING METHOD FOR REALISTIC CALCULATIONS OF INTERFACES

1985 ◽  
Vol 46 (C4) ◽  
pp. C4-321-C4-329 ◽  
Author(s):  
E. Molinari ◽  
G. B. Bachelet ◽  
M. Altarelli
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Matching Method

THE ATOMISTIC GREEN'S FUNCTION METHOD FOR INTERFACIAL PHONON TRANSPORT

2014 ◽  
Vol 17 (N/A) ◽  
pp. 89-145 ◽  
Author(s):  
Sridhar Sadasivam ◽  
Yuhang Che ◽  
Zhen Huang ◽  
Liang Chen ◽  
Satish Kumar ◽  
...  
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Phonon Transport ◽  
Green’S Function Method

THE EMPIRICAL GREEN’S FUNCTION TECHNIQUE MODIFICATION FOR ACCELEROGRAM SYNTHESIS IN LOWSEISMICITY REGIONS

2018 ◽  
Vol 12 (5-6) ◽  
pp. 72-80
Author(s):  
A. A. Krylov
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Main Shock ◽  
Amplitude Spectrum ◽  
Strong Motion ◽  
Function Technique ◽  
Focal Region ◽  
Empirical Green’S Function ◽  
Epicentral Zone ◽  
Empirical Green's Function

In the absence of strong motion records at the future construction sites, different theoretical and semi-empirical approaches are used to estimate the initial seismic vibrations of the soil. If there are records of weak earthquakes on the site and the parameters of the fault that generates the calculated earthquake are known, then the empirical Green’s function can be used. Initially, the empirical Green’s function method in the formulation of Irikura was applied for main shock record modelling using its aftershocks under the following conditions: the magnitude of the weak event is only 1–2 units smaller than the magnitude of the main shock; the focus of the weak event is localized in the focal region of a strong event, hearth, and it should be the same for both events. However, short-termed local instrumental seismological investigation, especially on seafloor, results usually with weak microearthquakes recordings. The magnitude of the observed micro-earthquakes is much lower than of the modeling event (more than 2). To test whether the method of the empirical Green’s function can be applied under these conditions, the accelerograms of the main shock of the earthquake in L'Aquila (6.04.09) with a magnitude Mw = 6.3 were modelled. The microearthquake with ML = 3,3 (21.05.2011) and unknown origin mechanism located in mainshock’s epicentral zone was used as the empirical Green’s function. It was concluded that the empirical Green’s function is to be preprocessed. The complex Fourier spectrum smoothing by moving average was suggested. After the smoothing the inverses Fourier transform results with new Green’s function. Thus, not only the amplitude spectrum is smoothed out, but also the phase spectrum. After such preliminary processing, the spectra of the calculated accelerograms and recorded correspond to each other much better. The modelling demonstrate good results within frequency range 0,1–10 Hz, considered usually for engineering seismological studies.

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