We present a numerical algorithm for an accurate and efficient computation of the convolution frequency domain layered media Green's function with given density function. Instead compressing matrix directly as in classical fast multipole, direct solver, H-matrix algorithms, this new considers translated form original so existing blocks from highly optimized free-space multipole method can be ea...

In this paper, we derive the time-fractional Cahn-Hilliard equation from continuum mixture theory with a modification of Fick's law diffusion. This model describes process phase separation nonlocal memory effects. We analyze existence, uniqueness, and regularity weak solutions equation. regard, consider degenerating mobility functions free energies Landau, Flory--Huggins double-obstacle type. a...

The modulus squared of a class of wave functions defined on phase space is used to define a generalized family of Q or Husimi functions. A parameter λ specifies orderings in a mapping from the operator |ψ〉〈σ| to the corresponding phase space wave function, where σ is a given fiducial vector. The choice λ = 0 specifies the Weyl mapping and the Q-function so obtained is the usual one when |σ〉 is ...

in this paper, numerical spline-based differential quadrature is presented for solving the boundary and initial value problems, and its application is used to solve the fixed rectangular membrane vibration equation. for the time integration of the problem, the runge–kutta and spline-based differential quadrature methods have been applied. the runge–kutta method was unstable for solving the prob...

This paper develops algorithms for the pricing of discretely sampled barrier, lookback and hindsight options and discretely exercisable American options. Under the Black-Scholes framework, the pricing of these options can be reduced to evaluation of a series of convolutions of the Gaussian distribution and a known function. We compute these convolutions efficiently using the double-exponential ...

Abstract Time-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since fully populated system matrices be computed for a large number of time steps or frequencies. In this article, we propose new approximation scheme Convolution Quadrature Method powered...