微分方程的小波配点法研究-计算数学专业论文.docxVIP

AbstraCteonveniently.认电enthe seaiing 丘metionhas no high- orde rderivative，the methodean beusedeffe etively.NumeriealexaJ叮Pleindleate sthatthe method15 ahigh effieient andhigh 一aceuratealgorithm .(3)Firstly，ourmethod15extendedtoone一dimensionaldlfl汕sloneq移ation，inwhichthe印atialdom ain 15disereted by eolloeation m ethod，叨d the syste m oford in娜dlfl贻rentialequation 15 solved by R un ge .kutta m eth o d，叨d tak ing the eonve ctive di且hslon e甲以ion，itshow th atthe m eth odre achedhigh er aceuracy.Seeondly，the m eth od15extende dto t场心一d而en-onalPD E ac eord ing 七刃o一tensorProduet、vavelat an alysis，which sho w that our m eth od has wideaPPlieab ility.K ey w ords:M ulti一resolutionAn alysis;玩terp olationBaseFun ction:从厄velet一collocationM eth -od:Two一tensorProduet夕目录目录1 绪论......................................................................................................................……，.........……11.1本文研究的背景及意义............................................................................................……11.1.1微分方程数值解概述......................................................................................……11.1.2 小波分析的发展..............................................................................................……31.2 基于小波分析的微分方程数值解研究进展............................................................……41.3 本文的工作................................................................................................................……62 泛函空间与小波基本理论..................................................................................................……82.1 泛函空间....................................................................................................................……82.1.1 距离空间..........................................................................................................……82.1.2 线性赋范空间..............……，.............................................................................……82.1.3 压lbe rt 空间.....................