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| h=input('请输入步长');
[x,u]=pro1(h);
function d=f(x,u)
d=exp(x)-100*u;
end
function [x,u] = pro1(h)
x1=0;
x2=1;
u1=1;
N=abs(x2-x1)/h;
u=zeros(N+1,1);
up=zeros(N+1,1);
x=zeros(N+1,1);
u(1)=u1;
up(1)=u1;
x(1)=x1;
for i = 1:N
up(i+1)=u(i)+f(x(i),u(i))*h;
uc=u(i)+f(x(i+1),up(i+1))*h;
u(i+1)=(uc+up(i+1))/2;
x(i+1)=x(i)+h;
disp(u(i+1));
end
syms z(t);
ys=dsolve(diff(z,t)==exp(t)-100*z,z(0)==1);
disp(ys)
subplot(2,2,1);
plot(x,u);
ylabel('改进Euler');
title('改进Euler函数');
subplot(2,2,2);
plot(x,up);
ylabel('Euler');
title('Euler函数');
subplot(2,2,3);
plot(u,up);
end
|
