In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...

We study linear stochastic evolution partial differential equations driven by additive noise. We present a general and flexible framework for representing the infinite dimensional Wiener process which is driving the equation. Since the eigenfunctions and eigenvalues of the covariance operator of the process are usually not available for computations, we propose an expansion in an arbitrary fram...

This paper characterizes the behavior of value functions in dynamic stochastic discounted programming models near fixed points of the state space. When the second derivative of the flow payoff function is bounded, the value function is proportional to a linear function plus xψδ . A specific formula for ψδ is provided, which implies ψδ continuously falls in the rate of patience. If the state var...

In frequency-domain optical diffusion imaging, the magnitude and the phase of modulated light propagated through a highly scattering medium are used to reconstruct an image of the scattering and absorption coefficients in the medium. Although current reconstruction algorithms have been applied with some success, there are opportunities for improving both the accuracy of the reconstructions and ...

The task of computer-based free-form shape design is fraught with practical and conceptual difficulties. Incorporating elements of traditional clay sculpting has long been recognised as a means of shielding a user from the complexities inherent in this form of modelling. The premise is to deform a mathematically-defined solid in a fashion that loosely simulates the physical moulding of an inela...

The Wheeler–DeWitt equation for a flat and compact Friedmann–Lemaître–Robertson–Walker cosmology at the pre-inflation epoch is studied in contexts of standard fractional quantum cosmology. Working within semiclassical regime applying Wentzel-Kramers-Brillouin (WKB) approximation, we show that some fascinating consequences are obtained our simple scenario completely different from their correspo...

This paper considers Schrödinger operators, and presents a probabilistic interpretation of the variation (or shape derivative) of the Dirichlet groundstate energy when the associated domain is perturbed. This interpretation relies on the distribution on the boundary of a stopped random process with Feynman-Kac weights. Practical computations require in addition the explicit approximation of the...

This paper addresses an approximation-based anti-windup (AW) control strategy for suppressing the windup effect caused by actuator saturation nonlinearity in proportional–integral–derivative (PID) controlled systems. The effect of actuator constraint is firstly regarded as a disturbance imported to the PID controller. The external disturbance can then be modeled by a linear differential equatio...