分数階拡散方程式の陰的数値解法(理論)

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  • An Implicit Numerical Method for Fractional Diffusion Equations
  • 分数階拡散方程式の陰的数値解法
  • ブンスウカイ カクサン ホウテイシキ ノ インテキ スウチ カイホウ

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This paper is concerned with a numerical method for solving a model equation of anomalous diffusion expressed with fractional integral with respect to the time variable t. In particular, a semi-discretization scheme derived from the application of the fractional trapezoidal rule proposed by Lubich in the mid 80's to the integral is examined. It is verified that the scheme converges in a special case where the exact solution is represented in a generalized Taylor form in fractional powers of t. Numerical examples are also presented which suggest convergence of the scheme in more general cases.(Theory)

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