Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Levy flight models whose jumps have infinite moments are mathematically used to describe the superdiffusion in complex systems. Exponentially tempering Levy measure of Levy flights leads to the tempered stable Levy processes which combine both the ?-stable and Gaussian trends; and the very large jumps are unlikely and all their moments exist. The probability density functions of the tempered stable Levy processes solve the tempered fractional diffusion equation.  focuses on designing the high order difference schemes for the tempered fractional diffusion equation on bounded domain. The high order difference approximations, called the tempered and ighted and shifted Grunwald difference (tempered-WSGD) operators, in space are obtained by using the properties of the tempered fractional calculus and ighting and shifting their first order Grunwald type difference approximations. And the Crank-Nicolson discretization is used in the time direction. The stability and convergence of the presented numerical schemes are established; and the numerical experiments are performed to confirm the theoretical results and testify the effectiveness of the schemes.
['Can Li', 'Weihua Deng']
I am writing a research paper on a idea High order schemes for the tempered fractional diffusion equations
[{"from": "human", "value": "I am writing a research paper on a idea High order schemes for the tempered fractional diffusion equations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Levy flight models whose jumps have infinite moments are mathematically used to describe the superdiffusion in complex systems. Exponentially tempering Levy measure of Levy flights leads to the tempered stable Levy processes which combine both the ?-stable and Gaussian trends; and the very large jumps are unlikely and all their moments exist. The probability density functions of the tempered stable Levy processes solve the tempered fractional diffusion equation.  focuses on designing the high order difference schemes for the tempered fractional diffusion equation on bounded domain. The high order difference approximations, called the tempered and ighted and shifted Grunwald difference (tempered-WSGD) operators, in space are obtained by using the properties of the tempered fractional calculus and ighting and shifting their first order Grunwald type difference approximations. And the Crank-Nicolson discretization is used in the time direction. The stability and convergence of the presented numerical schemes are established; and the numerical experiments are performed to confirm the theoretical results and testify the effectiveness of the schemes."}]