We propose two simple methods for numerically solving the Cauchy problem ordinary differential equations. They provide high accuracy and are suitable use in EXCEL other spreadsheets.

Neural Networks have been widely used to solve Partial Differential Equations. These methods require approximate definite integrals using quadrature rules. Here, we illustrate via 1D numerical examples the problems that may arise in these applications and propose different alternatives overcome them, namely: Monte Carlo methods, adaptive integration, polynomial approximations of Network output,...

The fair price of a financial option on an asset that follows a Poisson jump diffusion process satisfies a partial integro-differential equation. When numerical methods are used to solve such equations the integrals are usually evaluated using either quadrature methods or fast Fourier methods. Quadrature methods are expensive since the integrals must be evaluated at every point of the mesh. Tho...

In this paper, a method for differential encoding of odd-bit quadrature amplitude modulation (QAM) is presented. Differential encoding would allow QAM to be transmitted over media where coherent detection is not possible owing to phase ambiguity; it would allow such a transmission without the expense of the overhead incurred in data aided transmission. An example 32-QAM constellation is propose...

We analytically study received waveform asymmetries induced by chromatic dispersion (CD) for signed CD monitoring in differential quadrature phase-shift keying (DQPSK) systems and show that the asymmetries are results of differential detection and the ±π/4 phase shifters used in conventional DQPSK receivers. The theoretical insights developed help explain various published results on signed CD ...

*Correspondence: [email protected] Department of Science, Huaihai Institute of Technology, Cangwu Road, Lianyungang, 222005, China Abstract We apply the Chebyshev polynomial-based differential quadrature method to the solution of a fractional-order Riccati differential equation. The fractional derivative is described in the Caputo sense. We derive and utilize explicit expressions of weighting coef...

A Silicon-on-Insulator (SOI) Differential Quadrature Phase Shift Keying (DQPSK) demodulator based on a novel Multimode Interference (MMI) design is characterized for a number of operating wavelengths, with results indicating good uniformity and low wavelength dependency. Keywordssilicon integrated devices; DQPSK demodulator; MMI; characterization

The boundaries of the E ring can be fit by aligned Keplerian ellipses. Differential precession due to the quadrupole moment of Uranus tends to destroy the apse alignment. We propose that apse alignment is maintained by the self-gravity of the ring. The required ring mass -5 X 1018 g which corresponds to a surface density at quadrature -25 g cm-2•