经典R-K

yp.m:function dxdy=yp(x,y)dxdy=-2*y-4*x;ExpEulMtd.m:%Explicit Euler method%ExpEulMtdh=0.1;x=0:h:0.5;[row,col]=size(x);y=zeros(row,col);i=1;y(i)=2;for i=2:col    y(i)=y(i-1)+h*yp(x(i-1),y(i-1));endfigureplot(x,y)yClassicRKMtd.m%Classic R-K method%ClassicRKMtdh=0.1;x=0:h:0.5;[row,col]=size(x);y=zeros(row,col);i=1;y(i)=2;for i=2:col    k1=yp(x(i-1),y(i-1));        y_mid=y(i-1)+h*k1/2;    x_mid=x(i-1)+h/2;    k2=yp(x_mid,y_mid);     y_mid=y(i-1)+h*k2/2;    k3=yp(x_mid,y_mid);     y(i)=y(i-1)+h*k3;    k4=yp(x(i),y(i));    k_avg=(k1+2*k2+2*k3+k4)/6;    y(i)=y(i-1)+h*k_avg;    endfigureplot(x,y)ytrueSovle.m%trueSovleh=0.1;x=0:h:0.5;[row,col]=size(x);y=zeros(row,col);y=exp(-2*x)-2*x+1;figureplot(x,y)y

>> ClassicRKMtdy =    2.0000    1.6187    1.2703    0.9488    0.6493    0.3679>> trueSovley =    2.0000    1.6187    1.2703    0.9488    0.6493    0.3679>>