多步双变量Chebyshev谱配置方法求解初边值问题  

A Multi-Interval Bivariate Chebyshev Collocation Method For Solving Initial-Boundary Value Problem

作　　者：杨录峰 YANG Lu-feng(School of Mathematics and Information Science,North Minzu University, Yinchuan 750021, China)

机构地区：[1]北方民族大学数学与信息科学学院

出　　处：《数学的实践与认识》2018年第11期230-236,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11361002);宁夏高等学校一流学科建设资助项目(NXYLXK2017B09);北方民族大学科研项目(2016SXKY08)

摘　　要：提出了单步和多步双变量Chebyshev配置方法，用于求解非线性发展型偏微分方程的初边值问题．单步格式容易实施并且具有谱精度，并给出了多步方法的收敛性分析．数值实验表明：多步双变量Chebyshev谱配置方法在非线性发展型偏微分方程问题求解中是非常有效的，与理论分析一致，特别适合于长时间问题的数值模拟．In this paper,a single-interval and multi-interval bivariate Chebyshev collocation method are proposed for solving the initial-boundary value problems for the time-dependent nonlinear partial differential equation. The single scheme is easy implement and possesses the spectral accuracy. Thethe convergence of the multi-interval scheme is also given. The numerical results demonstrated the effectiveness and spectral accuracy of the multi-interval scheme for the nonlinear evolution partial differential equation and coincide well with the theoretical analysis, which is specially suitable for long-time calculation.

关 键 词：Chebyshev配置方法 双变量 谱精度 区域分解方法 初边值问题 

分 类 号：O175.8[理学—数学]