数值分析相关实验代码.docx

连续复合梯形和辛普森公式：function y=hanshu(x)y=(2*exp(-x)/sqrt(pi);x=0:0.01:1;h=0.01;futix=0;for n=1:100 y1=hanshu(x(n); y2=hanshu(x(n+1); futix=futix+(y1+y2)*h/2;endfutix=vpa(futix,6)fusim=0;for n=1:100 y1=hanshu(x(n); y2=hanshu(x(n+1); y3=hanshu(x(n)+x(n+1)/2); fusim=fusim+(y1+y2+4*y3)*h/6;endfusim=vpa(fusim,6)离散复合梯形和辛普森公式：x=0,1,4,9,16,25,36,49,64;y=0,1,2,3,4,5,6,7,8;plot(x,y,ro)x1=0:0.1:64;y1=interp1(x,y,x1,spline);hold onplot(x1,y1,b.)hold offftix=0;h=0.1;for n=1:length(x1)-1 ftix=ftix+(y1(n)+y1(n+1)*h/2;endftix=vpa(ftix,10)fsim=0;h=h*2;for n=1:2:length(x1)-2 fsim=fsim+(y1(n)+y1(n+2)+4*y1(n+1)*h/6;endfsim=vpa(fsim,10)改进的欧拉方法：function dy=hanshu(x,y)dy=1/x2-y/x;x=1:0.05:2;y(1)=1;h=0.05;for n=1:length(x)-1 y1=y(n)+h*hanshu(x(n),y(n); y(n+1)=y(n)+h*(hanshu(x(n),y(n)+hanshu(x(n)+h),y1)/2;endy龙格库塔方法：function dy=h(t,y)dy=zeros(3,1);dy(1)=-y(1);dy(2)=y(1)-10*y(2);dy(3)=-10*y(2);tspan=0:0.01:1;T,Y = ode45(h,tspan,1 1 1);plot(T,Y(:,1),-,T,Y(:,2),-.,T,Y(:,3),.)LU分解：A=1,2,3;2,5,2;3,1,5;b=14;18;20;if det(A)=0 error();else m,n=size(A); L=zeros(m,m); L=L+diag(ones(m,1); U=zeros(m,m); U(1,:)=A(1,:); L(2:end,1)=A(2:end,1)/U(1,1); for r=2:m U(r,r)=A(r,r)-L(r,1:r-1)*U(1:r-1,r); for i=r+1:m U(r,i)=A(r,i)-L(r,1:r-1)*U(1:r-1,i); L(i,r)=(A(i,r)-L(i,1:r-1)*U(1:r-1,r)/U(r,r); end endendLUy(1)=b(1);for i=2:n y(i)=b(i)-L(i,1:i-1)*y(1:i-1);endx(n)