抛物型方程非齐次边值问题的推广型LOD有限差分及有限元格式  

EXTENDED LOCALLY ONE-DIMENSIONAL FINITE DIFFERENCE AND FINITE ELEMENT SCHEMES FOR NONHOMOGENEOUS PARABOLIC DIFFERENTIAL EQUATIONS WITH NONHOMOGENEOUS BOUNDARY CONDITIONS

作　　者：王彩华[1] 王同科[1] 

机构地区：[1]天津师范大学数学科学学院,天津300384

出　　处：《高等学校计算数学学报》2006年第2期138-150,共13页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金项目(10471079)资助.

摘　　要：本文考虑区域Ω=[0，1]^d（d=2，3）上的非齐次抛物型方程第一边值问题δu/δt-CΔu＋C2u=f（x,t）,x∈Ω，t∈（0,T].This paper presents some extended locally one-dimensional finite difference and finite element schemes for nonhomogeneous parabolic differential equations with nonhomogeneous boundary conditions. It is proved that these finite difference schemes have second order accuracy with respect to discrete L^2 norm. Finally, the schemes are illustrated by numerical examples and the results are very satisfactory.

关 键 词：非齐次边值问题 抛物型方程 有限元格式 有限差分 LOD 第一边值问题 

分 类 号：O175.8[理学—数学] O175.26[理学—基础数学]