时间分数阶慢扩散方程的一类有效差分方法
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赵雅迪,吴立飞,杨晓忠,孙淑珍
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A Kind of Efficient Difference Method for the Time Fractional Sub-Diffusion Equation
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Yadi Zhao,Lifei Wu,Xiaozhong Yang,Shuzhen Sun
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表 3 E-I格式的误差和时间收敛阶$(m=80)$
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| | Implicit | | E-I | | $\alpha$ | $n$ | $L_{h, \tau}^2$ | Order2 | | $L_{h, \tau}^2$ | Order2 | | $0.7$ | 200 | 2.545864e-4 | — | | 1.094796e-4 | — | | 400 | 1.047661e-4 | 1.280984 | | 4.699933e-5 | 1.219950 | | 800 | 4.284855e-5 | 1.289853 | | 2.031905e-5 | 1.209807 | | 1600 | 1.746390e-5 | 1.294870 | | 8.822774e-6 | 1.203529 | | 3200 | 7.102732e-6 | 1.297930 | | 3.842242e-6 | 1.199284 | | $0.5$ | 200 | 8.475178e-5 | — | | 3.620591e-5 | — | | 400 | 3.023084e-5 | 1.487222 | | 1.351384e-5 | 1.421788 | | 800 | 1.072535e-5 | 1.494997 | | 5.109668e-6 | 1.403136 | | 1600 | 3.788677e-6 | 1.501259 | | 1.950831e-6 | 1.389141 | | 3200 | 1.332788e-6 | 1.507247 | | 7.514643e-7 | 1.376312 | | $0.4$ | 200 | 4.222321e-5 | — | | 1.920942e-5 | — | | 400 | 1.399031e-5 | 1.593609 | | 6.639797e-6 | 1.532603 | | 800 | 4.601493e-6 | 1.604254 | | 2.352434e-6 | 1.496985 | | 1600 | 1.501415e-6 | 1.615779 | | 8.522910e-7 | 1.464736 | | 3200 | 4.849225e-7 | 1.630497 | | 3.161945e-7 | 1.430534 |
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