| 带五次项的非线性Schrödinger方程的守恒差分格式 |
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| 引用本文： | 张法勇,安晓丽. 带五次项的非线性Schrödinger方程的守恒差分格式[J]. 计算数学, 2022, 44(1): 63-70. DOI: 10.12286/jssx.j2019-0557 |
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| 作者姓名： | 张法勇 安晓丽 |
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| 作者单位： | 黑龙江大学数学科学学院, 哈尔滨 150080 |
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| 基金项目： | 国家自然科学基金(10371077)资助. |
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| 摘 要： | 本文研究带有五次项的非线性Schrödinger方程初边值问题的有限差分法，其中方程中二阶偏导数项的系数、五次项的系数及初值满足下面的条件（1.6）.针对此问题，我们研究了一个守恒差分格式，在条件（1.6）下，差分解的$L^{infty}$模先验估计被得到.在此基础上，我们得到了差分解最优$L^2$模的误差估计.
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| 关 键 词： | 带五次项的非线性Schrödinger方程 守恒差分格式 |
| 收稿时间： | 2019-01-15 |
A CONSERVATIVE FINITE DIFFERENCE SCHEME FOR NONLINEAR SCHR(O)DINGER EQUATION INVOLVING QUINTIC TERMS |
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| Zhang Fayong,An Xiaoli. A CONSERVATIVE FINITE DIFFERENCE SCHEME FOR NONLINEAR SCHR(O)DINGER EQUATION INVOLVING QUINTIC TERMS[J]. Mathematica Numerica Sinica, 2022, 44(1): 63-70. DOI: 10.12286/jssx.j2019-0557 |
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| Authors: | Zhang Fayong An Xiaoli |
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| Affiliation: | School of Mathematical Sciences, Heilongjiang University, Harbin 150080, China |
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| Abstract: | In this paper,we shall study the finite difference method for the approximate solution of the initial-boundary value problem for the nonlinear Schrodinger equation involving quintic terms.We assume that the coefficient of second order partial derivative term,the coefficient of quintic and initial value uo satisfies the following condition(1.6).Due to this problem,we study a conservative difference scheme,priori estimates of the finite difference solutions on L∞norm are obtained,on this basis,error estimates of optimal order on L2norm of the finite difference solutions are obtained. |
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| Keywords: | nonlinear Schrodinger equation involving quintic terms conservative finite difference scheme |
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