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Numerical simulation of the soliton solutions for a complex modified Korteweg-de Vries equation by a finite difference method
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Tao Xu,Guowei Zhang,Liqun Wang,Xiangmin Xu,Min Li
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Table 2. Time error analysis of three one-soliton solutions with mesh step h = 0.001 and different time steps.
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| Time step | e∞ (SH soliton) | Order | e∞ (DH soliton) | Order | e∞ (MH soliton) | Order |
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| τ=0.1 | 7.41E-5 | — | 8.36E-5 | — | 5.70E-4 | — | | $\tau =\tfrac{0.1}{2}$ | 1.86E-5 | 1.9977 | 2.10E-5 | 1.9989 | 1.43E-4 | 1.9944 | | $\tau =\tfrac{0.1}{4}$ | 4.68E-6 | 1.9957 | 5.26E-6 | 1.9921 | 3.59E-5 | 1.9921 | | $\tau =\tfrac{0.1}{8}$ | 1.26E-6 | 1.9784 | 1.34E-6 | 1.9921 | 9.08E-6 | 1.9852 | | $\tau =\tfrac{0.1}{16}$ | 5.94E-7 | 1.9083 | 3.70E-7 | 1.7270 | 2.42E-6 | 1.9063 |
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