Abstract
In this article one of the fractional partial differential equations was solved by finite difference scheme based on five point and three point central space method with discretization in time. We use between the Caputo and the Riemann-Liouville derivative definition and the Grünwald-Letnikov operator for the fractional calculus. The stability analysis of this scheme is examined by using von-Neumann method. A comparison between exact solutions and numerical solutions is made. Some figures and tables are included.
Highlights
Anomalous equation is a diffusion process with a nonlinear relationship to time contrary to typical diffusion process, connected with the interactions within the complex and non- homogeneous background
In contrast to typical diffusion, anomalous diffusion is described by a power law [1]
4, we apply the method to fractional diffusion equation with the given initial and boundary conditions and compared the numerical solutions with the exact results
Summary
Anomalous equation is a diffusion process with a nonlinear relationship to time contrary to typical diffusion process, connected with the interactions within the complex and non- homogeneous background. On the other hand this phenomena is observed in heat baths [2], diffusion through porous material [3,4], nuclear magnetic resonance diffusometry in disordered materials [4], behaviour of polymers in a glass transition [5,6]and particle dynamics inside polymer network [7].Fractional order linear and nonlinear differential equations were examined by some researchers by using different methods [8,9,10,11,12]. 4, we apply the method to fractional diffusion equation with the given initial and boundary conditions and compared the numerical solutions with the exact results
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