13、0,0,0,0,1,4,1,0,2,0,0,0,0,0,2,4,0,0,2,0,0,0,1,0,0,4,2,0,1,0,0,0,1,0,1,4,1,0,1,0,0,0,1,0,2,4,0,0,1,0,0,0,2,0,0,4,2,0,0,0,0,0,2,0,1,4,1,0,0,0,0,0,2,0,2,4,g,g,g,g,g,g,g,g,h,U,U,U,U,U,U,U,U,U,24,椭圆型方程的五点差分格式,令,则矩阵方程为,B,I,I,B,I,I,B,A,I,B,2,2,1,1,1,4,2,1,4,1,2,4,T,g,g,g,g,g,g,g,g,g,9,8,7,6,4,3,2,1,2,2,0,2 。

14、,2,T,U,U,U,U,U,U,U,U,U,U,9,8,7,6,5,4,3,2,1,hg,AU,2,25,椭圆型方程的五点差分格式,3.3,混合,Robins,边值条件,0,2,2,2,2,y,x,y,x,n,u,y,x,u,y,x,y,x,y,u,x,u,其中,0,y,x,y,x,26,椭圆型方程的五点差分格式,例,1,用五点差分格式求解,Laplace,方程,在区域,内的近似解 ， 边界值为,取,0,2,2,2,2,y,u,x,u,4,0,4,0,y,x,y,x,4,0,0,4,80,0,y,y,u,y,u,4,0,180,4,0,0,x,x,u,x,u,y,1,y,x,h,27,椭圆型方程 。

15、的五点差分格式,解,网格节点如图所示,U,10,U,11,U,12,U,7,U,8,U,9,U,4,U,5,U,6,U,1,U,2,U,3,u(1,4)=180 u(2,4)=180 u(3,4)=180,u(0,3)=80,u(0,2)=80,u(0,1)=80,u(0,0)=80,u(4,3)=0,u(4,2)=0,u(4,1)=0,u(4,0)=0,28,椭圆型方程的五点差分格式,180,4,180,4,260,4,0,4,0,4,80,4,0,4,0,4,80,4,0,2,4,0,2,4,80,2,4,12,11,9,12,11,10,8,11,10,7,12,9,8,6,11,9,8 。

16、,7,5,10,8,7,4,9,6,5,3,8,6,5,4,2,7,5,4,1,6,3,2,5,3,2,1,4,2,1,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,29,椭圆型方程的五点差分格式,180,180,260,0,0,80,0,0,80,0,0,80,4,1,0,1,0,0,0,0,0,0,0,0,1,4,1,0,1,0,0,0,0,0,0,0,0,1,4,0,0,1,0,0,0,0,0,0,1,0,0,4,1,0,1,0,0,0,0,0,0,1 。

17、,0,1,4,1,0,1,0,0,0,0,0,0,1,0,1,4,0,0,1,0,0,0,0,0,0,1,0,0,4,1,0,1,0,0,0,0,0,0,1,0,1,4,1,0,1,0,0,0,0,0,0,1,0,1,4,0,0,1,0,0,0,0,0,0,2,0,0,4,1,0,0,0,0,0,0,0,0,2,0,1,4,1,0,0,0,0,0,0,0,0,2,0,1,4,12,11,10,9,8,7,6,5,4,3,2,1,U,U,U,U,U,U,U,U,U,U,U,U,30,椭圆型方程的五点差分格式,1,0,0,0,1,0,0,0,1,4,1,0,1,4,1,0,1,4,2,I,B,B, 。

18、I,I,B,I,I,B,I,I,B,A,其中,T,K,180,180,260,0,0,80,0,0,80,0,0,80,31,椭圆型方程的五点差分格式,解矩阵方程,AU = K,U= 71.8218 56.8543 32.2342,75.2165 61.6806 36.0412,87.3636 78.6103 50.2502,115.6276 115.1468 86.3492,T,32,椭圆型方程的五点差分格式,33,椭圆型方程的五点差分格式,34,椭圆型方程的五点差分格式,35,椭圆型方程的五点差分格式,作业,1,P.115,例,3.1,取,h=1/3,利用五点,差分格式写出求解节点上的,U,l,m,值的线,性方程组及矩阵方程,2,P.159,习题三,2,36 。

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标题：五点|五点差分格式课件( 二 )