1、宋玉霞 2008050216 統數 信科0802 實驗二：五點差分格式一、 實驗題目：二、 實驗要求：用五點差分格式求解橢圓型偏微分方程三、 程序運行結果：U = Columns 1 through 9 0.3426 0.6516 0.8968 1.0543 1.1086 1.0543 0.8968 0.6516 0.3426Columns 10 through 18 0.3793 0.7216 0.9931 1.1675 1.2276 1.1675 0.9931 0.7216 0.3793Columns 19 through 27 0.4198 0.7985 1.0990 1.2920 1.

2、3585 1.2920 1.0990 0.7985 0.4198Columns 28 through 36 0.4643 0.8832 1.2156 1.4291 1.5026 1.4291 1.2156 0.8832 0.4643Columns 37 through 45 0.5134 0.9766 1.3442 1.5802 1.6615 1.5802 1.3442 0.9766 0.5134 Columns 46 through 54 0.5676 1.0796 1.4860 1.7469 1.8368 1.7469 1.4860 1.0796 0.5676Columns 55 thro

3、ugh 63 0.6274 1.1934 1.6425 1.9309 2.0303 1.9309 1.6425 1.1934 0.6274 Columns 64 through 72 0.6934 1.3189 1.8153 2.1340 2.2439 2.1340 1.8153 1.3189 0.6934Columns 73 through 81 0.7663 1.4575 2.0061 2.3583 2.4797 2.3583 2.0061 1.4575 0.7663 Columns 82 through 90 0.8467 1.6106 2.2168 2.6060 2.7401 2.60

4、60 2.2168 1.6106 0.8467 Columns 91 through 99 0.9356 1.7796 2.4494 2.8795 3.0277 2.8795 2.4494 1.7796 0.9356 Columns 100 through 108 1.0337 1.9662 2.7062 3.1814 3.3451 3.1814 2.7062 1.9662 1.0337 Columns 109 through 117 1.1420 2.1722 2.9897 3.5146 3.6955 3.5146 2.9897 2.1722 1.1420 Columns 118 throu

5、gh 126 1.2615 2.3995 3.3026 3.8824 4.0822 3.8824 3.3026 2.3995 1.2615 Columns 127 through 135 1.3933 2.6502 3.6477 4.2881 4.5088 4.2881 3.6477 2.6502 1.3933Columns 136 through 144 1.5387 2.9267 4.0283 4.7356 4.9793 4.7356 4.0283 2.9267 1.5387 Columns 145 through 153 1.6989 3.2315 4.4478 5.2288 5.497

6、8 5.2288 4.4478 3.2315 1.6989 Columns 154 through 162 1.8754 3.5673 4.9100 5.7720 6.0690 5.7720 4.9100 3.5673 1.8754 Columns 163 through 171 2.0697 3.9368 5.4186 6.3699 6.6977 6.3699 5.4186 3.9368 2.0697四、程序附錄：1 .function z=g1x(x)%求下邊界z=0;2. function z=g2x(x)%求上邊界z=0;3. function z=g1y(y)%求左邊界PI=3.14

7、15926;z=sin(PI*y);4. function z=g2y(y)%求右邊界PI=3.1415926;z=sin(PI*y)*exp(2);5. function ff=f(x,y)%求右端函數PI=3.1415926;ff=(PI2-1)*exp(x)*sin(PI*y);6. function cl=fclt(a,b,c,d,h1,h2)%求Fx=a:h1:b;y=c:h2:d;m=length(x);n=length(y);cl(1)=f(x(2),y(2)+1/h22*g1x(x(2)+1/h12*g1y(y(2);%求含兩個邊界點的F(共4個點)cl(n-2)=f(x(2)

8、,y(n-1)+1/h12*g1y(y(n-1)+1/h22*g2x(x(2);cl(m-3)*(n-2)+1)=f(x(m-1),y(2)+1/h22*g1x(x(m-1)+1/h12*g2y(y(2);cl(n-2)*(m-2)=f(x(m-1),y(n-1)+1/h12*g2y(y(n-1)+1/h22*g2x(x(m-1);for i=2:n-3%求含一個邊界點的F(左右) cl(i)=f(x(2),y(i+1)+1/h12*g1y(y(i+1); cl(m-3)*(n-2)+i)=f(x(m-1),y(i+1)+1/h12*g2y(y(i+1);endfor i=2:m-3%求含一個

9、邊界點的F(上下)cl(i-1)*(n-2)+1)=f(x(i+1),y(2)+1/h22*g1x(x(i+1);cl(i*(n-2)=f(x(i+1),y(n-1)+1/h22*g2x(x(i+1);endfor i=3:m-2%求內點的F for j=3:n-2 cl(i-2)*(n-2)+(j-1)=f(x(i),y(j); end end7. function y=tril1(A,B,C,n)%求AA，n為A的個數n1,n1=size(C);%求C的階數for i=2:n-1 y(i-1)*n1+1:i*n1,(i-2)*n1+1:(i-1)*n1)=C; y(i-1)*n1+1:i*n1,(i-1)*n1+1:i*n1)=A; y(i-1)*n1+1:i*n1,i*n1+1:(i+1)*n1)=B;endy(1:n1,1:n1)=A;y(1:n1,n1+1:2*n1)=B;y(n-1)*n1+1:n*n1,(n-2)*n1+1:(n-1)*n1)=C;y(n-1)*n1+1:n*n1,(n-1)*n1+1:n*n1)=A;8. a=0;b=2;c=0;d=1;%主函數，用五點差分格式求數值解h1=0.1;h2=0.1;x=a:h1:b;t=c:h2:d;m=length(x);n=length(t);A=diag(2/h