The coupled nonlinear Schrödinger equation models several intersting physical phenomena. It presents a model equation for optical fiber with linear birefringence. In this paper, we present a linearly implicit conservative method to solve this equation. This method is second order accurate in...

The Several numerical techniques have been developed and compared for solving the one-dimensional and three-dimentional advection-diffusion equation with constant coefficients. the subject has played very important roles to fluid dynamics as well as many other field of science and engineering....

We present an acceleration technique, effective for explicit finite difference schemes describing diffusive processes with nearly symmetric operators, called Super-Time-Stepping (STS). The technique is applied to the two-factor problem of option pricing under stochastic volatility. It is shown...

We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating sequence solves an optimal stopping problem for geometric...

Several finite difference schemes are discussed for solving the two-dimensional Schrodinger equation with Dirichlet’s boundary conditions. We use three fully implicit finite difference schemes, two fully explicit finite difference techniques, an alternating direction implicit procedure and the...

The seismic ground motion of a test area in the eastern district of Naples is computed with a hybrid technique based on the mode summation and the finite difference methods. This technique allows us the realistic modelling of source and propagation effects, including local soil conditions. In...

We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating sequence solves an optimal stopping problem for geometric...

This paper investigates computational and implementation issues for the valuation of options on three underlying assets, focusing on the use of the finite difference methods. We demonstrate that implicit methods, which have good convergence and stability prooperties, can now be implemented...

This paper proposes an efficient model for the term structure of interest rates when the interest rate takes very small values. We make the following choices: (i) we model the short-term interest rate, (ii) we assume that once the interest rate reaches zero, it stays there and we have to wait...

This paper examines the effects of uncertainty through dynamic learning about the firm's project value in the real options framework. We extend the real options framework with incomplete information by allowing an unobserved state variable that drives profits to follow a stochastic process with...