摘要
振动有限差分(PFD)方法,既离散徽商项也离散非微商项(包括微商系数),在微商用直接差分近似的前提下提高差分格式的精度和分辨率.PFD方法包括局部线化微分方程的摄动精确数值解(PENS)方法和摄动数值解(PNS)方法以及考虑非线性近似的摄动高精度差分(PHD)方法。论述了这些方法的基本思想、具体技巧、若干方程(对流扩散方程、对流扩散反应方程、双曲方程、抛物方程和KdV方程)的PENS、PNS和PHD格式,它们的性质及数值实验.并与有关的数值方法作了必要的比较.最后提出值得进一步研究的一些课题.
In the perturbation finite difference (PFD) method both the differentials and non- differential terms in the differential equation studied are discretized. High accuracy and high resolution difference schemes are obtained with the differentials being approximated by the direct differences (i.e., second-order-accurate center difference and first-order-accurate upwind difference). PFD method includes the perturbation exact numerical solution (PENS) scheme for locally lin- earized differential equation and the perturbation high-order-accurate difference (PHD) schemes with nonlinear effects. The basic idea and concrete technique of PFD method and some PENS-, PNS-and PHD- schemes for some differential equations including the convective-diffusion equation, convective- diffusion- react ion equation, hyperbolic equation, parabolic equation and K dV equation are summarized. The properties and typical numerical results of the above-mentioned schemes are discussed, comparisons of PFD method with the Other related numerical methods are made and some subjects for further studies are presented.
出处
《力学进展》
EI
CSCD
北大核心
2000年第2期200-215,共16页
Advances in Mechanics
基金
国家自然科学基金
中国科学院"九五"基础性研究重大项目
中国科学院力学研究所所长基金
中国科学院力学研究所LHD实验室项目
关键词
有限差分方法
摄动精确数值解
摄动有限差分方法
finite difference method, perturbation finite difference method, perturbation exact numerical solution scheme, perturbation high-order-accurate difference scheme