Anomalous diffusion simulation method based on discrete fraction order difference

An analog method and anomalous diffusion technology, applied in complex mathematical operations, electrical digital data processing, special data processing applications, etc., can solve problems such as long-term or long-term calculation difficulties

Inactive Publication Date: 2015-03-04
NEIJIANG NORMAL UNIV
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Problems solved by technology

[0004] The purpose of the present invention is to provide a method for simulating anomalous diffusion based on discrete fractional difference, which solves the problem that the genetic characteristics of classical fractional derivative operators lead to long history of anomalous diffusion or difficult calculation for a long time

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  • Anomalous diffusion simulation method based on discrete fraction order difference
  • Anomalous diffusion simulation method based on discrete fraction order difference
  • Anomalous diffusion simulation method based on discrete fraction order difference

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[0039] The present invention will be described in detail below in combination with specific embodiments.

[0040] The invention provides a numerical simulation method for discretizing the diffusion problem by utilizing the fractional order difference on the time scale. The mathematical model of the simulation method is based on the discrete fractional diffusion problem, which is a general expression of the traditional diffusion equation. The discrete fractional diffusion equation proposed by the invention has discrete memory effect, simple expression form, easy parameter control, and can be widely used in image processing, pollution control, groundwater transmission, fabric heat transfer, gas diffusion and other fields.

[0041] The present invention adopts the following one-dimensional classical diffusion equation describing the diffusion phenomenon:

[0042] u t (x,t)=Ku xx (x,t) (1)

[0043] K is the diffusion coefficient, and u(x,t) represents the concentration functio...

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Abstract

The invention discloses an anomalous diffusion simulation method based on a discrete fraction order difference. The anomalous diffusion simulation method based on the discrete fraction order difference includes: using a one dimension classical diffusion equation for describing a diffusion phenomenon; defining the discrete fraction order difference, using the discrete fraction order difference to discretize the one dimension classical diffusion equation, and performing numerical simulation according to initial boundary conditions. Compared with a diffusion model built by using a classical fraction order diffusion equation, a diffusion model built by using the anomalous diffusion simulation method based on the discrete fraction order difference is concise in expression, and convenient and fast in numerical simulation on the premise of maintaining discrete memory effects.

Description

technical field [0001] The invention belongs to the technical field of numerical simulation, and relates to an anomalous diffusion simulation method based on discrete fractional difference. Background technique [0002] The diffusion equation is commonly used to describe the natural heat and mass transfer phenomena. For porous media such as fabric, coal and rock mass, soil, etc., the fluid often exhibits the characteristics of anomalous diffusion. Fractional derivatives are consistent with the characteristics of anomalous diffusion due to their genetic characteristics. Recently, fractional derivatives have been used to modify the diffusion equation, and many researchers have proposed time-fractional diffusion equations [1-4] , which is used to describe the complexity of fluid diffusion in porous media, avoiding the description of the complex structure of porous media. [0003] However, the heredity of fractional derivative operators makes it difficult to calculate the lon...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F19/00G06F17/11
Inventor 吴国成曾生达杜米特鲁·伯莱亚努黄蓝蓝
Owner NEIJIANG NORMAL UNIV
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