A third order numerical scheme for the two-dimensional sine-Gordon equation
A third order numerical scheme for the two-dimensional sine-Gordon equation
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DOI：
10.1016/j.matcom.2006.11.004
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发表时间：
2007-12
期刊：
影响因子：
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通讯作者：
A. G. Bratsos
中科院分区：
文献类型：
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作者：
A. G. Bratsos
利用一个三阶有理逼近，将二维sine-Gordon（SG）方程转化为一个二阶初值问题，并将其应用于一个三次递推关系.由此产生的非线性有限差分格式，这是分析的稳定性，解决了适当的预测-校正（P-C）计划，其中的预测是一个显式的二阶。该方案通过使用修改（MPC）来加速，其中已经评估的值用于校正器。对SG方程的线孤子和环孤子进行了数值计算，得到了无阻尼和有阻尼两种情况下P-C/MPC格式的结果。
A rational approximant of third order, which is applied to a three-time level recurrence relation, is used to transform the two-dimensional sine-Gordon (SG) equation into a second-order initial-value problem. The resulting nonlinear finite-difference scheme, which is analyzed for stability, is solved by an appropriate predictor–corrector (P–C) scheme, in which the predictor is an explicit one of second order. This scheme is accelerated by using a modification (MPC) in which the already evaluated values are used for the corrector. The behavior of the proposed P–C/MPC schemes is tested numerically on the line and ring solitons known from the bibliography, regarding SG equation and conclusions for both the mentioned schemes regarding the undamped and the damped problem are derived.