单摆方程流程图

Z(i)=Z(i-1)+h*(Z1(i)+2*Z2(i)+2*Z3(i)+Z4(i))/6Y(i)=Y(i-1)+h*(Y1(i)+2*Y2(i)+2*Y3(i)+Y4(i))/6

Z4(i)=f(Y(i-1)+h*Y3(i))Y4(i)=Z(i-1)+h*Z3(i)

Z2(i)=f(Y(i-1)+0.5h*Y1(i))Y2(i)=Z(i-1)+0.5h*Z1(i)

i=i+1

显式欧拉法

Y(i)=Y(i-1)+h*Z(i-1)Z(i)=Y(i-1)+h*f(Y(i-1))

四阶经典龙格-库塔法

(Z=Θ'，Y=Θ)

Q10公式

(预测)Y_(i)=Y(i-1)+h*Z(i-1)Z_(i)=Y(i-1)+h*f(Y(i-1))

…

(校正)Z(i)=Z(i-1)+0.5h*(f(Y_(i-1))+f(Y(i-1))Y_(i)=Y(i-1)+0.5h*(Z(i-1)+Z_(i-1))

Z1(i)=f(Y(n-1))Y1(i)=Z(i-1)

Z3(i)=f(Y(i-1)+0.5h*Y2(i))Y3(i)=Z(i-1)+0.5h*Z2(i)

改进欧拉法