A New Implicit Finite Difference Method for Solving Time Fractional Diffusion Equation
سال انتشار: 1397
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 118
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شناسه ملی سند علمی:
JR_IJMAC-8-1_001
تاریخ نمایه سازی: 28 دی 1401
چکیده مقاله:
In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order ۰ < a< ۱ (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in the Caputo sense. We propose a new finite difference method for solving time fractional diffu- sion equation. In our method firstly, we transform the Caputo derivative into Riemann-Liovill derivative. The stability and convergence of this method are investigated by a Fourier analysis. We show that this method is uncondition- ally stable and convergent with the convergence order O( ۲+h۲), where t and h are time and space steps respectively. Finally, a numerical example is given that confirms our theoretical analysis and the behavior of error is examined to verify the order of convergence.
کلیدواژه ها:
fractional derivative ، finite difference method ، Stability and convergence ، Fourier analysis ، time fractional diffusion equation
نویسندگان
elham afshari
Islamic Azad University,khomain Branch