Highly efficient difference methods for stochastic space fractional wave equation driven by additive and multiplicative noise

2021 ◽  
Vol 116 ◽  
pp. 106988
Author(s):  
Yanjiao Zhou ◽  
Jianqiang Xie ◽  
Zhiyue Zhang
Keyword(s):  
Wave Equation ◽  
Multiplicative Noise ◽  
Fractional Wave Equation ◽  
Highly Efficient ◽  
Additive And Multiplicative Noise ◽  
Stochastic Space ◽  
Difference Methods

scholarly journals Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1329
Author(s):  
Lev Ryashko ◽  
Dmitri V. Alexandrov ◽  
Irina Bashkirtseva
Keyword(s):  
Multiplicative Noise ◽  
Nonlinear Dynamical Systems ◽  
Stochastic Theory ◽  
Slow Variable ◽  
Theoretical Description ◽  
Mathematical Study ◽  
Stochastic Generation ◽  
Nonlinear Dynamical ◽  
Additive And Multiplicative Noise ◽  
And Shifts

A problem of the noise-induced generation and shifts of phantom attractors in nonlinear dynamical systems is considered. On the basis of the model describing interaction of the climate and vegetation we study the probabilistic mechanisms of noise-induced systematic shifts in global temperature both upward (“warming”) and downward (“freezing”). These shifts are associated with changes in the area of Earth covered by vegetation. The mathematical study of these noise-induced phenomena is performed within the framework of the stochastic theory of phantom attractors in slow-fast systems. We give a theoretical description of stochastic generation and shifts of phantom attractors based on the method of freezing a slow variable and averaging a fast one. The probabilistic mechanisms of oppositely directed shifts caused by additive and multiplicative noise are discussed.

scholarly journals Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ming-Sheng Hu ◽  
Ravi P. Agarwal ◽  
Xiao-Jun Yang
Keyword(s):  
Wave Equation ◽  
Fourier Series ◽  
Series Solution ◽  
Differential Operators ◽  
Fractional Wave Equation ◽  
Local Fractional Calculus ◽  
Vibrating String ◽  
Fractional Differential ◽  
Fractional Differential Operators

We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. By applying this technique we derive the local fractional Fourier series solution of the local fractional wave equation in fractal vibrating string and show the fundamental role of the Mittag-Leffler function.

scholarly journals GPS Signal Detection under Multiplicative and Additive Noise

2012 ◽  
Vol 66 (4) ◽  
pp. 479-500 ◽  
Author(s):  
P. Huang ◽  
Y. Pi ◽  
I. Progri
Keyword(s):  
Signal Detection ◽  
Urban Areas ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Power Level ◽  
Signal Propagation ◽  
Signal Acquisition ◽  
Detection Scheme ◽  
Additive And Multiplicative Noise ◽  
Gps Signal Acquisition

In some Global Positioning System (GPS) signal propagation environments, especially in the ionosphere and urban areas with heavy multipath, GPS signal encounters not only additive noise but also multiplicative noise. In this paper we compare and contrast the conventional GPS signal acquisition method which focuses on handling GPS signal acquisition with additive noise, with the enhanced GPS signal processing under multiplicative noise by proposing an extension of the GPS detection mechanism, to include the GPS detection model that explains detection of the GPS signal under additive and multiplicative noise. For this purpose, a novel GPS signal detection scheme based on high order cyclostationarity is proposed. The principle is introduced, the GPS signal detection structure is described, the ambiguity of initial PseudoRandom Noise (PRN) code phase and Doppler shift of GPS signal is analysed. From the simulation results, the received GPS signal at low power level, which is degraded by additive and multiplicative noise, can be detected under the condition that the received block of GPS data length is at least 1·6 ms and sampling frequency is at least 5 MHz.

Regularization of a backward problem for the inhomogeneous time‐fractional wave equation

2020 ◽  
Vol 43 (8) ◽  
pp. 5450-5463
Author(s):  
Nguyen Huy Tuan ◽  
Vo Au ◽  
Le Nhat Huynh ◽  
Yong Zhou
Keyword(s):  
Wave Equation ◽  
Fractional Wave Equation ◽  
Backward Problem ◽  
Time Fractional Wave Equation

scholarly journals On the Fractional Wave Equation

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 874
Author(s):  
Francesco Iafrate ◽  
Enzo Orsingher
Keyword(s):  
Brownian Motion ◽  
Wave Equation ◽  
Wave Equations ◽  
Stable Process ◽  
Space Time ◽  
Probabilistic Interpretation ◽  
Symmetric Stable Process ◽  
Fractional Wave Equation ◽  
Fractional Wave Equations ◽  
Time Fractional Wave Equation

In this paper we study the time-fractional wave equation of order 1 < ν < 2 and give a probabilistic interpretation of its solution. In the case 0 < ν < 1 , d = 1 , the solution can be interpreted as a time-changed Brownian motion, while for 1 < ν < 2 it coincides with the density of a symmetric stable process of order 2 / ν . We give here an interpretation of the fractional wave equation for d > 1 in terms of laws of stable d−dimensional processes. We give a hint at the case of a fractional wave equation for ν > 2 and also at space-time fractional wave equations.

scholarly journals Nonparametric estimation in a regression model with additive and multiplicative noise

2020 ◽  
Vol 380 ◽  
pp. 112971 ◽  
Author(s):  
Christophe Chesneau ◽  
Salima El Kolei ◽  
Junke Kou ◽  
Fabien Navarro
Keyword(s):  
Regression Model ◽  
Nonparametric Estimation ◽  
Multiplicative Noise ◽  
Additive And Multiplicative Noise
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