微分方程数值解 五点差分格式

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1、宋玉霞2008050216统数信科0802实验二：五点差分格式一、实验题目：二、实验要求：用五点差分格式求解椭圆型偏微分方程三、程序运行结果：U=Columns1through90.34260.65160.89681.05431.10861.05430.89680.65160.3426Columns10through180.37930.72160.99311.16751.22761.16750.99310.72160.3793Columns19through270.41980.79851.09901.29201.35851.29201.09900.79850.419

2、8Columns28through360.46430.88321.21561.42911.50261.42911.21560.88320.4643Columns37through450.51340.97661.34421.58021.66151.58021.34420.97660.5134Columns46through540.56761.07961.48601.74691.83681.74691.48601.07960.5676Columns55through630.62741.19341.64251.93092.03031.93091.64251.19340.6

3、274Columns64through720.69341.31891.81532.13402.24392.13401.81531.31890.6934Columns73through810.76631.45752.00612.35832.47972.35832.00611.45750.7663Columns82through900.84671.61062.21682.60602.74012.60602.21681.61060.8467Columns91through990.93561.77962.44942.87953.02772.87952.44941.77960

4、.9356Columns100through1081.03371.96622.70623.18143.34513.18142.70621.96621.0337Columns109through1171.14202.17222.98973.51463.69553.51462.98972.17221.1420Columns118through1261.26152.39953.30263.88244.08223.88243.30262.39951.2615Columns127through1351.39332.65023.64774.28814.50884.28813.6

5、4772.65021.3933Columns136through1441.53872.92674.02834.73564.97934.73564.02832.92671.5387Columns145through1531.69893.23154.44785.22885.49785.22884.44783.23151.6989Columns154through1621.87543.56734.91005.77206.06905.77204.91003.56731.8754Columns163through1712.06973.93685.41866.36996.697

6、76.36995.41863.93682.0697四、程序附录：1.functionz=g1x(x)%求下边界z=0;2.functionz=g2x(x)%求上边界z=0;3.functionz=g1y(y)%求左边界PI=3.1415926;z=sin(PI*y);4.functionz=g2y(y)%求右边界PI=3.1415926;z=sin(PI*y)*exp(2);5.functionff=f(x,y)%求右端函数PI=3.1415926;ff=(PI^2-1)*exp(x)*sin(PI*y);6.functioncl=fclt(a,b,c,d,h1,h

7、2)%求Fx=a:h1:b;y=c:h2:d;m=length(x);n=length(y);cl(1)=f(x(2),y(2))+1/h2^2*g1x(x(2))+1/h1^2*g1y(y(2));%求含两个边界点的F(共4个点)cl(n-2)=f(x(2),y(n-1))+1/h1^2*g1y(y(n-1))+1/h2^2*g2x(x(2));cl((m-3)*(n-2)+1)=f(x(m-1),y(2))+1/h2^2*g1x(x(m-1))+1/h1^2*g2y(y(2));cl((n-2)*(m-2))=f(x(m-1),y(n-1))+1/h1^2*