差分方程的第一次试验.doc

差分方程的第一次试验（解常微分方程）y-y=x,y(0)=1;y(1)=e+1/e-1=2.086161269630488 .解析解为y=ex+e(-x)-x;数值解法：差分方程#include /消元形式的追赶法解线性方程组，对主对角有的矩阵不能解#include /此次写出了很多毛病 一定要注意仔细分析 特别是矩阵的输入 一定要注意草稿要做好int main(void)double a10000,b10000,c10000,d10000;long i,n;double x10000,x0,xn,h,y0,yn,y10000;printf(请输入自变量范围：n);scanf(%lf%lf,&x0,&xn);printf(请输入边值：n);scanf(%lf%lf,&y0,&yn);printf(请输入分段数：n);scanf(%ld,&n);n=n-1;h=(xn-x0)/(n+1);x0=x0+h;a0=0;cn-1=0;b0=-(2+h*h);c0=1;d0=h*h*x0-y0;for(i=1;i=n-2;i+)xi=xi-1+h;ai=1;bi=-(2+h*h);ci=1;di=h*h*xi;xn-1=xn-2+h;an-1=1;bn-1=-(2+h*h);dn-1=h*h*xn-1-yn;an-1=1;bn-1=-(2+h*h);dn-1=h*h*xn-1-yn;for(i=0;i=0;i-)yi=(di-ci*yi+1)/bi;printf(原方程组的解为：n);for(i=0;i y=exp(x)+exp(-x)-x;x,yans = 1.000000000000000 2.086161269630488 0.990000000000000 2.072811163371308 0.980000000000000 2.059767340780817 0.970000000000000 2.047027497457552 0.960000000000000 2.034589359398230 0.950000000000000 2.022450682770347 0.940000000000000 2.010609253687793 0.930000000000000 1.999062887989456 0.920000000000000 1.987809431020812 0.910000000000000 1.976846757418453 0.900000000000000 1.966172770897549 0.890000000000000 1.955785404042220 0.880000000000000 1.945682618098791 0.870000000000000 1.935862402771916 0.860000000000000 1.926322776023544 0.850000000000000 1.917061783874718 0.840000000000000 1.908077500210172 0.830000000000000 1.899368026585718 0.820000000000000 1.890931492038406 0.810000000000000 1.882766052899413 0.800000000000000 1.874869892609689 0.790000000000000 1.867241221538293 0.780000000000000 1.859878276803425 0.770000000000000 1.852779322096143 0.760000000000000 1.845942647506728 0.750000000000000 1.839366569353690 0.740000000000000 1.833049430015399 0.730000000000000 1.826989597764325 0.720000000000000 1.821185466603859 0.710000000000000 1.815635456107716 0.700000000000000 1.810338011261886 0.690000000000000 1.805291602309138 0.680000000000000 1.800494724596037 0.670000000000000 1.795945898422482 0.660000000000000 1.791643668893731 0.650000000000000 1.787586605774913 0.640000000000000 1.783773303348000 0.630000000000000 1.780202380271240 0.620000000000000 1.776872479441017 0.610000000000000 1.773782267856138 0.600000000000000 1.770930436484535 0.590000000000000 1.768315700132364 0.580000000000000 1.765936797315475 0.570000000000000 1.763792490133272 0.560000000000000 1.761881564144916 0.550000000000000 1.760202828247882 0.540000000000000 1.758755114558848 0.530000000000000 1.757537278296906 0.520000000000000 1.756548197669081 0.510000000000000 1.755786773758152 0.500000000000000 1.755251930412761 0.490000000000000 1.754942614139795 0.480000000000000 1.754857793999034 0.470000000000000 1.754996461500061 0.460000000000000 1.755357630501408 0.450000000000000 1.755940337111942 0.440000000000000 1.756743639594478 0.430000000000000 1.757766618271598 0.420000000000000 1.759008375433691 0.410000000000000 1.760468035249173 0.400000000000000 1.762144743676910 0.390000000000000 1.764037668380807 0.380000000000000 1.766145998646580 0.370000000000000 1.768468945300679 0.360000000000000 1.771005740631372 0.350000000000000 1.773755638311970 0.340000000000000 1.776717913326204 0.330000000000000 1.779891861895707 0.320000000000000 1.783276801409648 0.310000000000000 1.786872070356467 0.300000000000000 1.790677028257721 0.290000000000000 1.794691055604037 0.280000000000000 1.798913553793162 0.270000000000000 1.803343945070101 0.260000000000000 1.807981672469338 0.250000000000000 1.812826199759146 0.240000000000000 1.817877011387958 0.230000000000000 1.823133612432812 0.220000000000000 1.828595528549859 0.210000000000000 1.834262305926930 0.200000000000000 1.840133511238152 0.190000000000000 1.846208731600614 0.180000000000000 1.852487574533082 0.170000000000000 1.858969667916750 0.160000000000000 1.865654659958022 0.150000000000000 1.872542219153341 0.140000000000000 1.879632034256033 0.130000000000000 1.886923814245183 0.120000000000000 1.894417288296533 0.110000000000000 1.902112205755400 0.100000000000000 1.910008336111607 0.090000000000000 1.918105468976439 0.080000000000000 1.926403414061594 0.070000000000000 1.934902001160165 0.060000000000000 1.943601080129608 0.050000000000000 1.952500520876738 0.040000000000000 1.961600213344712 0.030000000000000 1.970900067502025 0.020000000000000 1.980400013333511 0.010000000000000 1.990100000833336 0 2.000000000000000对比可知：到达尾部时，精度达到10-5-10-6.02, 0.001,20001.999000 5.518141422640184 exp(1.999)+exp(-1.999)-1.999ans