Numerical study of blow-up to the purely elliptic generalized Davey-Stewartson system
Numerical study of blow-up to the purely elliptic generalized Davey-Stewartson system
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DOI：
10.1016/j.cam.2016.12.003
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发表时间：
2017-06
期刊：
影响因子：
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通讯作者：
Gulcin M. Muslu
中科院分区：
文献类型：
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作者：
Gulcin M. Muslu
利用松弛数值方法研究了纯椭圆型广义Davey-Stewartson方程组的爆破解。数值方法是基于一个隐式有限差分格式的二阶精度在时间和空间。通过考察平面波解的线性稳定性，分析了数值方法的稳定性。为了评估松弛方法检测爆破的能力，对几个测试问题进行了数值模拟。特别注意了差距区间，既没有建立整体存在性，也没有建立爆破结果。数值研究了爆破时间随耦合参数的单调性。
Blow-up solutions for the purely elliptic generalized Davey–Stewartson system are studied by using a relaxation numerical method. The numerical method is based on an implicit finite-difference scheme with a second-order accuracy in both time and space. The stability of the numerical method is analyzed by investigating the linear stability of plane wave solutions. To evaluate the ability of the relaxation method to detect blow-up, numerical simulations are conducted for several test problems. A particular attention is paid to the gap interval neither a global existence nor a blow-up result is established. The monotonicity properties of blow-up time on the coupling parameter are also investigated numerically.