| 非线性Schrödinger方程的一个线性化紧致差分格式 |
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| 引用本文： | 王廷春.非线性Schrödinger方程的一个线性化紧致差分格式[J].南京气象学院学报,2012,4(6):569-572. |
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| 作者姓名： | 王廷春 |
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| 作者单位： | 南京信息工程大学 数学与统计学院,南京,210044 |
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| 基金项目： | 国家自然科学基金(41174165;1112 6292) |
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| 摘 要： | 对非线性Schrödinger方程给出了一个线性化紧致差分格式,运用不动点定理和能量方法证明了格式的唯一可解性,还运用能量方法和数学归纳法,避开困难的先验估计,证明格式在空间方向和时间方向分别具有四阶和二阶精度,数值算例验证了格式的精度和数值稳定性.
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| 关 键 词： | 非线性Schrö dinger方程 紧致差分格式 存在唯一性 收敛性 |
| 收稿时间： | 2012/4/21 0:00:00 |
A linearized compact difference scheme for nonlinear Schrödinger equation |
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| WANG Tingchun.A linearized compact difference scheme for nonlinear Schrödinger equation[J].Journal of Nanjing Institute of Meteorology,2012,4(6):569-572. |
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| Authors: | WANG Tingchun |
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| Institution: | School of Mathematics and Statistics,Nanjing University of Information Science & Technology,Nanjing 210044 |
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| Abstract: | We propose a linearized compact difference scheme for the nonlinear Schrödinger equation.The existence of the difference solution is proved by Brouwer fixed point theorem.It is proved by the discrete energy method and the method of mathematical induction that the new scheme is uniquely solvable and convergent with fourth-order in x-direction and second-order in t-direction.Numerical results verify the precision and numerical stability of the proposed scheme. |
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| Keywords: | nonlinear Schrö dinger equation compact difference scheme unique solvability convergence |
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