时间分数阶扩散方程线性三角形元的高精度分析
|
|
史艳华,张亚东,王芬玲,赵艳敏,王萍莉
|
High Accuracy Analysis of Linear Triangular Element for Time Fractional Diffusion Equations
|
|
Yanhua Shi,Yadong Zhang,Fenling Wang,Yanmin Zhao,Pingli Wang
|
|
表 4 ‖取不同\alpha时在空间方向的误差和收敛阶
|
| |
|
| \alpha | h | t_{n}=0.2 | 阶 | t_{n}=0.4 | 阶 | t_{n}=0.7 | 阶 | t_{n}=0.9 | 阶 | | 1/4 | 5.310e-02 | / | 1.103e-01 | / | 1.982e-01 | / | 2.575e-01 | / | | 1/8 | 1.387e-02 | 1.937 | 2.894e-02 | 1.930 | 5.217e-02 | 1.925 | 6.790e-02 | 1.923 | | 0.3 | 1/16 | 3.506e-03 | 1.984 | 7.324e-03 | 1.982 | 1.321e-02 | 1.981 | 1.720e-02 | 1.981 | | 1/32 | 8.791e-04 | 1.995 | 1.837e-03 | 1.996 | 3.315e-03 | 1.995 | 4.316e-03 | 1.995 | | 1/4 | 4.606e-02 | / | 1.028e-01 | / | 1.926e-01 | / | 2.538e-01 | / | | 1/8 | 1.183e-02 | 1.961 | 2.673e-02 | 1.944 | 5.048e-02 | 1.932 | 6.676e-02 | 1.927 | | 0.6 | 1/16 | 2.977e-03 | 1.990 | 6.749e-03 | 1.986 | 1.277e-02 | 1.983 | 1.690e-02 | 1.982 | | 1/32 | 7.457e-04 | 1.997 | 1.691e-03 | 1.996 | 3.202e-03 | 1.996 | 4.240e-03 | 1.995 | | 1/4 | 3.674e-02 | / | 9.320e-02 | / | 1.870e-01 | / | 2.514e-01 | / | | 1/8 | 9.223e-03 | 1.994 | 2.389e-02 | 1.964 | 4.872e-02 | 1.940 | 6.593e-02 | 1.931 | | 0.9 | 1/16 | 2.311e-03 | 1.997 | 6.012e-03 | 1.991 | 1.231e-02 | 1.985 | 1.668e-02 | 1.983 | | 1/32 | 5.781e-04 | 1.999 | 1.505e-03 | 1.998 | 3.085e-03 | 1.996 | 4.182e-03 | 1.996 |
|
|
|