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Nonlinear Schrödinger equation with a Dirac delta potential: finite difference method*
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Bin Cheng(程彬),Ya-Ming Chen(陈亚铭),Chuan-Fu Xu(徐传福),Da-Li Li(李大力),Xiao-Gang Deng(邓小刚)
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Table 4. Accuracy test for equation (1) with g = 1 and $\lambda =-0.7$ at time t = 1. Here, N1 = N2 = N.
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| p | q |
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| N | L2 error | Rate | ${L}^{\infty }$ error | Rate | L2 error | Rate | ${L}^{\infty }$ error | Rate |
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| 200 | 5.92E-04 | | 1.22E-03 | | 1.55E-03 | | 1.90E-03 | | | 400 | 1.48E-04 | 2.00 | 3.04E-04 | 2.00 | 3.93E-04 | 1.98 | 4.88E-04 | 1.96 | | 800 | 3.82E-05 | 1.95 | 7.49E-05 | 2.02 | 9.94E-05 | 1.98 | 1.24E-04 | 1.97 | | 1600 | 9.80E-06 | 1.96 | 1.85E-05 | 2.02 | 2.50E-05 | 1.99 | 3.11E-05 | 1.99 |
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