1、實驗二(習題2.2)1、題目2用Crank-Nicolson差分格式計算拋物型方程=520 ： x ： 1t2:t：x滿足初始條件 u|t=si n二x 0_x_1 和邊界條件 u lx=u 1x4 = 0 t 0 在t =0.1,0.2處的解，.：t =k =0.1,. ：x =h =0.1。2、程序#i nclude#in cludeconst double pi=3.1415926;const int N=11;const int M=11;const double t=0.1;const double h=0.1;const double e=2.71828;double Ut(dou

2、ble x); 初始時刻值double Ux1(double time);/ 左邊值double Ux2(double time);/ 右邊值double FUN(double x,double time);void mai n()int i,k;double U1111,d9;double a,b,T1,T n,r;double g9,w9;cout ab;cout T1T n;r=t/(h*h);for(k=0;k11;k+)Uk0=Ux1(T1+t*k);Uk10=Ux2(T1+t*k);for(i=0;i11;i+)U0i=Ut(a+h*i);for(k=1;k11;k+)計算方程常數(shù)

3、項 d0=(1-r)*Uk-10+0.5*r*Uk-11;d8=(1-r)*Uk-19+0.5*r*Uk-18; for(i=1;i8;i+)di=(1-r)*Uk-1i+0.5*r*(Uk-1i+1+Uk-1i-1); g0=d0/(1+r);w0=0.5*r/(1+r); for(i=1;i0;i-)Uki=gi-1+wi-1*Uki+1;cout古典顯格式計算結(jié)果(t=0.1,h=0.1): n;for(i=0;i11;i+)coutU1i ;coutn;cout精確計算結(jié)果(t=0.1,h=0.1): n; for(i=0;iN;i+)coutFUN(a+i*h,0.1) ;coutn

4、; cout古典顯格式計算結(jié)果(t=0.2 h=0.1): n;for(i=0;i11;i+)coutU2i ;coutn;cout精確計算結(jié)果(t=0.2,h=0.1): n; for(i=0;iN;i+)coutFUN(a+i*h,0.2) ;coutn;double Ut(double x) 初始時刻值if(x-i nt(x)=O)x=0;return (si n( pi*x);double Ux1(double time)/左邊值return 0;double Ux2(double time)/右 邊值return 0;double FUN(double x,double time)

5、double s1,s2;if(x-i nt(x)=0) x=0;s1=-pow(pi,2)*time;s2=pow(e,s1)*s in (pi*x);return s2;3、運行結(jié)果節(jié)點t=0.1t=0.2數(shù)值解真解數(shù)值解真解000000.10.2647750.1151730.128410.0429260.20.2734880.2190720.01772720.081650.30.3053450.3015270.1136970.1123820.40.3382490.3544660.1545650.1321130.50.3561930.3727080.1642280.1389110.60.3482590.3544660.1540490.1321130.70.3078640.3015270.1293180.1123820.80.2319270.2190720.09325980.081650.90.1197650.1151730.04982320.042926100004、結(jié)果分析Crank-Nicolson格式（六點對稱格式）在各個網(wǎng)格節(jié)點處對t,x的差商方法分別為,：:u k 2u