摘要
BasedontheTaylorseriesmethodandLi’sspatialdifferentialmethod,ahigh-orderhybridTaylor–Lischemeisproposed.Theresultsofalinearadvectionequationindicatethat,usingtheinitialvaluesofthesquare-wavetype,aresultwiththirdorderaccuracyoccurs.However,usinginitialvaluesassociatedwiththeGaussianfunctiontype,aresultwithveryhighprecisionappears.Thestudydemonstratesthat,whentheorderofthetimeintegralismorethanthree,thecorrespondingoptimalspatialdifferenceordercouldbehigherthansix.Theresultsindicatethatthereasonforwhythereisnoimprovementrelatedtoanorderofspatialdifferenceabovesixistheuseofatimeintegralschemethatisnothighenough.TheauthoralsoproposesarecursivedifferentialmethodtoimprovetheTaylor–Lischeme’scomputationspeed.Amorerapidandhighprecisionprogramthandirectcomputationofthehigh-orderspacedifferentialitemisemployed,andthecomputationspeedisdramaticallyboosted.Basedonamultiple-precisionlibrary,theultrahigh-orderTaylor–LischemecanbeusedtosolvetheadvectionequationandBurgers’equation.
出版日期
2017年12月22日（中国期刊网平台首次上网日期，不代表论文的发表时间）
