耦合Schrödinger--KdV系统数值格式的收敛性
Convergence of a numerical scheme for a coupled Schrödinger--KdV system
AI总结：
通过截断技巧和能量估计，证明了有界域上耦合Schrödinger--KdV系统有限差分半离散格式在强范数下的收敛性，并给出数值算例。
摘要：
我们证明了在有界域上逼近耦合Schrödinger--KdV系统的有限差分半离散格式在强范数下的收敛性。该系统模拟了短波和长波的相互作用。由于连续情况下的能量估计不适用于离散情形，我们依赖于一个合适的截断问题，并证明该截断问题可还原为原始问题。我们给出了一些数值算例来说明我们的收敛性结果。
英文摘要：
We prove the convergence in a strong norm of a finite difference semi-discrete scheme approximating a coupled Schrödinger--KdV system on a bounded domain. This system models the interaction of short and long waves. Since the energy estimates available in the continuous case do not carry over to the discrete setting, we rely on a suitably truncated problem which we prove reduces to the original one. We present some numerical examples to illustrate our convergence result.
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