摘要
本文主要讨论带非局部粘性项水波方程的数值方法.我们建立了一种求解这类粘性水波方程的数值方案.该方案有效解决了非局部粘性项与非线性项的离散问题.所提的格式包括对α阶分数阶项的2-α阶格式和对非线性项的线性化处理的混合格式.我们证明了这种格式是无条件稳定的,并得出线性Crank-Nicolson加2-α格式的收敛阶是O(?t32+N1-m)的结论.一系列的数值例子验证了理论证明的正确性.最后,我们用所提数值格式研究了粘性水波方程的渐近衰减率,并讨论了各种参数项对衰减率的影响.
we focus on the numerical investigation of a water wave model with a nonlocal vis- cous dispersive term. We construct and analyze a schema to numerically solving the nonlocal water wave model. The key for the success consists in a particular combination of the treatments for the nonlocal dispersive term and nonlinear convection term. The proposed methods employ a known （2 - a）-order schema for the a-order fractional derivative and a mixed linearization of the nonlinear term. A rigorous analysis shows that the proposed schema is unconditionally stable, and the linearized Crank-Nicolson plus （2 - α）-order schemes is O（Δt32＋N1-m）. A series of numerical examples is presented proposed methods are used to investigate nonlocal viscous wave equation, as well as to confirm the theoretical prediction. Finally the the asymptotical decay rate of the solutions of the the impact of different terms on this decay rate.
出处
《工程数学学报》
CSCD
北大核心
2015年第4期577-589,共13页
Chinese Journal of Engineering Mathematics
基金
国家自然科学基金(11461012)
温州医科大学科研课题项目(QTJ11014)
浙江省教育厅科研资助项目(Y201328047)~~
关键词
分数阶
无条件稳定
有限差分法
谱方法
衰减率
fractional order
unconditionally stable
finite difference methods
spectral methods
decay rate
