1 %数值解常微分方程欧拉算法
 2 %例子：dyfun=inline(\'y-2*x/y\');[x,y]=euler2(dyfun,[0,1],1,0.2);
 3 %输入：函数dfun(x,y)，求解区间xspan[x0,xN]，初值y0，步长h
 4 %输出：节点x，数值解y
 5 function [x,y]=euler2(dyfun,xspan,y0,h)
 6 x=xspan(1):h:xspan(2);y(1)=y0;
 7 for n=1:length(x)-1
 8     y(n+1)=y(n)+h*feval(dyfun,x(n),y(n));
 9 end
10 x=x\';y=y\';
11 end

 1 %数值解常微分后退欧拉法算法
 2 %例子：dfun=inline(\'x+y\',\'x\',\'y\');[x,y]=eulerh1(dfun,0,1,0.02,5)
 3 %输入：函数dfun(x,y)，初值x0,y0,步长h,维度N
 4 %输出：结点x和数值解y
 5 function [x,y]=eulerh1(dfun,x0,y0,h,N)
 6 x=zeros(1,N+1);
 7 y=zeros(1,N+1);
 8 x(1)=x0;y(1)=y0;
 9 for n=1:N
10     x(n+1)=x(n)+h;
11     z0=y(n)+h*dfun(x(n),y(n));
12     for k=1:3
13         z1=y(n)+h*dfun(x(n+1),z0);
14         if abs(z1-z0)<1e-6
15             break;
16         end
17         z0=z1;
18     end
19     y(n+1)=z1;
20 end

 1 %数值解常微分梯形欧拉法算法
 2 %例子：dfun=inline(\'x+y\',\'x\',\'y\');[x,y]=eulert(dfun,0,1,0.02,5)
 3 %输入：函数dfun(x,y)，初值x0,y0,步长h,维度N
 4 %输出：结点x和数值解y
 5 function [x,y]=eulert(dfun,x0,y0,h,N)
 6 x=zeros(1,N+1);
 7 y=zeros(1,N+1);
 8 x(1)=x0;y(1)=y0;
 9 for n=1:N
10     x(n+1)=x(n)+h;
11     z0=y(n)+h*dfun(x(n),y(n));
12     for k=1:3
13         z1=y(n)+(h/2)*(dfun(x(n),y(n))+dfun(x(n+1),z0));
14         if abs(z1-z0)<1e-6
15             break;
16         end
17         z0=z1;
18     end
19     y(n+1)=z1;
20 end

 1 %数值解常微分改进欧拉法算法
 2 %例子：dfun=inline(\'x+y\',\'x\',\'y\');[x,y]=eulerh1(dfun,0,1,0.02,5)
 3 %输入：函数dfun(x,y)，初值x0,y0,步长h,维度N
 4 %输出：结点x和数值解y
 5 function [x,y]=eulerg2(dfun,x0,y0,h,N)
 6 x=zeros(1,N+1);
 7 y=zeros(1,N+1);
 8 x(1)=x0;y(1)=y0;
 9 for n=1:N
10     x(n+1)=x(n)+h;
11     ybar=y(n)+h*dfun(x(n),y(n));
12     y(n+1)=y(n)+(h/2)*(dfun(x(n),y(n))+dfun(x(n+1),ybar));
13 end
14 end