二维分数阶发展型方程的正式的二阶BDF交替方向隐式紧致差分格式

Abstract

Abstract: In this paper, we will consider a formally second-order backward differentiation formula (BDF) compact alternating direction implicit (ADI) difference scheme for the twodimensional fractional evolution equation. To obtain a fully discrete implicit scheme, the integral term is treated by means of the second order convolution quadrature suggested by Lubich and the second order space derivatives are approximated by the fourth-order accuracy compact finite difference. The stability and convergence of the compact difference scheme in a new norm are proved by the energy method. The verification of stability and convergence is based on the nonnegative character of the real quadratic form associated with the convolution quadrature. A numerical experiment in total agreement with our analysis is reported.

Key words: Two-dimensional fractional evolution equation, Second-order BDF ADI, Compact difference scheme, Stability, Convergence

CLC Number:

O241.82

Chen Hongbin, Gan Siqing, Xu Da, Peng Yulong. A Formally Second-Order BDF Compact ADI Difference Scheme for the Two-Dimensional Fractional Evolution Equation[J].Acta mathematica scientia,Series A, 2017, 37(5): 976-992.

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A Formally Second-Order BDF Compact ADI Difference Scheme for the Two-Dimensional Fractional Evolution Equation

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