func6p12.m

来自「数值分析最常用的四十种算法」· M 代码 · 共 24 行

%func6p12.m常微分初值问题
s=0,t=1,n=100,y1=2
a=linspace(s,t,n)
x=t-s
h=(t-s)/n
%Euler Rule
for i=1:n-1
    y11=y1+x/n*sub6p12(a(i),y1)
    y1=y1+x/n/2*(sub6p12(a(i),y1)+sub6p12(a(i+1),y11))
    disp(i)
end
%R-K Rule
y1=2
for i=1:n-1
    k1=sub6p12(a(i),y1)*h
    k2=sub6p12(a(i)+h/2,y1+k1/2)*h
    k3=sub6p12(a(i)+h/2,y1+k2/2)*h
    k4=sub6p12(a(i)+h,y1+k3)*h
    y1=y1+(k1+2*k2+2*k3+k4)/6
    disp(i)
end
%True Value:y(1)=1.41421356237310,y(0.5)=1.78885438199983
%Euler Rule:y(1)=1.41913670503394,y(0.5)=1.79443366894940
%R-K Methom:y(1)=1.41915871762530,y(0.5)=1.79446130391271,依然是R-K方法略优于Euler