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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 1. Spatial error analysis of three one-soliton solutions with time step τ=0.01 and different mesh sizes.
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| Mesh size | e∞ (SH soliton) | Order | e∞ (DH soliton) | Order | e∞ (MH soliton) | Order |
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| h = 0.1 | 1.36E-3 | — | 5.98E-4 | — | 4.26E-3 | — | | $h=\tfrac{0.1}{2}$ | 3.41E-4 | 1.9977 | 1.50E-5 | 1.9966 | 1.06E-3 | 2.0030 | | $h=\tfrac{0.1}{4}$ | 8.55E-5 | 1.9957 | 3.76E-5 | 1.9934 | 2.69E-4 | 1.9835 | | $h=\tfrac{0.1}{8}$ | 2.17E-5 | 1.9784 | 9.61E-6 | 1.9747 | 6.85E-5 | 1.9742 | | $h=\tfrac{0.1}{16}$ | 5.78E-6 | 1.9083 | 2.90E-6 | 1.8750 | 1.80E-5 | 1.9298 |
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