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| A NEW CLASS OF UNIFORMLY SECOND ORDERACCURATE DIFFRENCE SCHEMES FOR 2D SCALAR CONSERVATION LAWS | |
| 摘 要： | 1.ConvergenceofAClassofUniformlySecondorderAccurateDifferenceSchemesInthissection,weconsidertheCauchyproblemfornonlinearhyperbolicscalarconservationlawswithtwospacevariables:&u+&f(u)+Ovg(u)=o,u(t,xly)eR,tE(O,T),(x,y)ER',(1.1)u(o,x,y)=uo(x,y),(x,y)ER',(1t2)wherefandg:R-+RareLipschitzcontinuousfunctionsandtheinitialdatauoisaboundedfunctionwithcompactsupport.LetAt,ax,Aybethe.time,x-spaceandy-spaceincremelltsofthediscretizationrespectively.Themeshratios,,A.=at/Ax,A.=At/ay,wil1bekeptconst… |
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