Anomalous Diffusion Equations with Multiplicative Acceleration

Saenko, V. V.

doi:10.1134/s1063776118030202

Cited by 2 publications

(5 citation statements)

References 71 publications

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“…To obtain the master equation of the CTRW process, we use the approach proposed in the paper [48] and further developed in the paper [49]. Consider the collision density f (r, p, t), where r is the radius of the particle vector, p is the particle impulse, and t is time.…”

Section: Master Equation Of the Ctrw Processmentioning

confidence: 99%

“…Without losing generality, we will assume that m = 1. It was shown in the paper [49] that if there are n discrete states, the value f (r, v, t) can be presented in the form…”

Section: Master Equation Of the Ctrw Processmentioning

confidence: 99%

“…To construct a histogram, the trajectory is modeled until the condition is met (49). As soon as this condition ceases to be met, the trajectory is terminated, and the contribution from this trajectory is calculated…”

Section: The Solution To the Equation Of Anomalous Diffusionmentioning

confidence: 99%

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Numerical Method for Solving of the Anomalous Diffusion Equation Based on a Local Estimate of the Monte Carlo Method

et al. 2022

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This paper considers a method of stochastic solution to the anomalous diffusion equation with a fractional derivative with respect to both time and coordinates. To this end, the process of a random walk of a particle is considered, and a master equation describing the distribution of particles is obtained. It has been shown that in the asymptotics of large times, this process is described by the equation of anomalous diffusion, with a fractional derivative in both time and coordinates. The method has been proposed for local estimation of the solution to the anomalous diffusion equation based on the simulation of random walk trajectories of a particle. The advantage of the proposed method is the opportunity to estimate the solution directly at a given point. This excludes the systematic component of the error from the calculation results and allows constructing the solution as a smooth function of the coordinate.

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Section: Master Equation Of the Ctrw Processmentioning

confidence: 99%

“…Without losing generality, we will assume that m = 1. It was shown in the paper [49] that if there are n discrete states, the value f (r, v, t) can be presented in the form…”

Section: Master Equation Of the Ctrw Processmentioning

confidence: 99%

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Numerical Method for Solving of the Anomalous Diffusion Equation Based on a Local Estimate of the Monte Carlo Method

et al. 2022

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“…To obtain the kinetic equation, we will use the approach proposed in the paper [28], which was developed in the paper [47]. We will consider the density of collisions f (r, p, t), where r is the radius-vector of the particle, p-is the particle momentum, t-is time.…”

Section: Kinetic Equation Of the Random Walk Processmentioning

confidence: 99%

“…Without loss of generality, we assume that m = 1. The paper [47] shows that, with the presence n of discrete states, the value f (r, v, t) can be represented in the form:…”

Section: Kinetic Equation Of the Random Walk Processmentioning

confidence: 99%

Numerical Solution to Anomalous Diffusion Equations for Levy Walks

et al. 2021

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The process of Levy random walks is considered in view of the constant velocity of a particle. A kinetic equation is obtained that describes the process of walks, and fractional differential equations are obtained that describe the asymptotic behavior of the process. It is shown that, in the case of finite and infinite mathematical expectation of paths, these equations have a completely different form. To solve the obtained equations, the method of local estimation of the Monte Carlo method is described. The solution algorithm is described and the advantages and disadvantages of the considered method are indicated.

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Anomalous Diffusion Equations with Multiplicative Acceleration

Cited by 2 publications

References 71 publications

Numerical Method for Solving of the Anomalous Diffusion Equation Based on a Local Estimate of the Monte Carlo Method

Numerical Method for Solving of the Anomalous Diffusion Equation Based on a Local Estimate of the Monte Carlo Method

Numerical Solution to Anomalous Diffusion Equations for Levy Walks

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