Search results for "finite difference"

Generalized finite difference schemes with higher order Whitney forms

2021

Finite difference kind of schemes are popular in approximating wave propagation problems in finite dimensional spaces. While Yee’s original paper on the finite difference method is already from the sixties, mathematically there still remains questions which are not yet satisfactorily covered. In this paper, we address two issues of this kind. Firstly, in the literature Yee’s scheme is constructed separately for each particular type of wave problem. Here, we explicitly generalize the Yee scheme to a class of wave problems that covers at large physics field theories. For this we introduce Yee’s scheme for all problems of a class characterised on a Minkowski manifold by (i) a pair of first ord…

Operator splitting methods for American option pricing

2004

Abstract We propose operator splitting methods for solving the linear complementarity problems arising from the pricing of American options. The space discretization of the underlying Black-Scholes Scholes equation is done using a central finite-difference scheme. The time discretization as well as the operator splittings are based on the Crank-Nicolson method and the two-step backward differentiation formula. Numerical experiments show that the operator splitting methodology is much more efficient than the projected SOR, while the accuracy of both methods are similar.

Finite difference time domain simulation of soil ionization in grounding systems under lightning surge conditions

2004

This paper proposes a Maxwell’s equations finite difference time domain (FDTD) approach for electromagnetic transients in ground electrodes in order to take into account the non linear effects due to soil ionization. A time variable soil resistivity method is used in order to simulate the soil breakdown, without the formulation of an initial hypothesis about the geometrical shape of the ionized zone around the electrodes. The model has been validated by comparing the computed results with available data found in technical literature referred to concentrated earths. Some application examples referred to complex grounding systems are reported to show the computational capability of the propos…

Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation

2004

A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.

Numerical analysis of thermally induced optical nonlinearity in GaSe layered crystal

1996

A numerical approach to studying thermally induced optical nonlinearity in semiconductors is presented. A transient finite difference algorithm is applied to solve the thermal diffusion equation coupled with the nonlinear absorbance-transmittance of Au/GaSe/Au samples with an applied electric field. The presented analysis can deal with any arbitrary axisymmetric dependence of the input power over the sample and external electric field, and provides information about the steady state and transitory effects in the transmittance.

On the Efficacy of PCM to Shave Peak Temperature of Crystalline Photovoltaic Panels: An FDM Model and Field Validation

2013

The exploitation of renewable energy sources and specifically photovoltaic (PV) devices have been showing significant growth; however, for a more effective development of this technology it is essential to have higher energy conversion performances. PV producers often declare a higher efficiency respect to real conditions and this deviation is mainly due to the difference between nominal and real temperature conditions of the PV. In order to improve the solar cell energy conversion efficiency many authors have proposed a methodology to keep the temperature of a PV system lower: a modified crystalline PV system built with a normal PV panel coupled with a Phase Change Material (PCM) heat stor…

An IMEX-Scheme for Pricing Options under Stochastic Volatility Models with Jumps

2014

Partial integro-differential equation (PIDE) formulations are often preferable for pricing options under models with stochastic volatility and jumps, especially for American-style option contracts. We consider the pricing of options under such models, namely the Bates model and the so-called stochastic volatility with contemporaneous jumps (SVCJ) model. The nonlocality of the jump terms in these models leads to matrices with full matrix blocks. Standard discretization methods are not viable directly since they would require the inversion of such a matrix. Instead, we adopt a two-step implicit-explicit (IMEX) time discretization scheme, the IMEX-CNAB scheme, where the jump term is treated ex…

Multipactor radiation analysis within a waveguide region based on a frequency-domain representation of the dynamics of charged particles

2009

[EN] A technique for the accurate computation of the electromagnetic fields radiated by a charged particle moving within a parallel-plate waveguide is presented. Based on a transformation of the time-varying current density of the particle into a time-harmonic current density, this technique allows the evaluation of the radiated electromagnetic fields both in the frequency and time domains, as well as in the near- and far-field regions. For this purpose, several accelerated versions of the parallel-plate Green's function in the frequency domain have been considered. The theory has been successfully applied to the multipactor discharge occurring within a two metal-plates region. The proposed…

CARATTERIZZAZIONE ELETTROMAGNETICA DEL COMPORTAMENTO DINAMICO DI ELETTRODI INTERRATI IN PRESENZA DI IONIZZAZIONE DEL TERRENO

2009

Solution strategies for 1D elastic continuum with long-range interactions: Smooth and fractional decay

2010

Abstract An elastic continuum model with long-range forces is addressed in this study within the context of approximate analytical methods. Such a model stems from a mechanically-based approach to non-local theory where long-range central forces are introduced between non-adjacent volume elements. Specifically, long-range forces depend on the relative displacement, on the volume product between interacting elements and they are proportional to a proper, material-dependent, distance-decaying function. Smooth-decay functions lead to integro-differential governing equations whereas hypersingular, fractional-decay functions lead to a fractional differential governing equation of Marchaud type. …