解微分方程算法C语言程序(精心整理版).pdf

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解微分方程算法C语言程序（精心整理版）

#includestdio.h

#includestdlib.h

#includemath.h

#includegraphics.h

floatk1,k2,k3,k4,m1,m2,m3,m4,n1,n2,n3,n4;

floatt,ts,tf,h;

floatx[1001],y[1001],z[1001],x_axis[1001];

intcount;

voidinitial()

{

x[0]=1.0;

y[0]=-1.0;

z[0]=0.0;

ts=0.0;

tf=20.0;

count=500;

}

voidrunge()

{

inti=0;

h=(tf-ts)/count;

for(i=1;i=count;i++)

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解微分方程算法C语言程序(精心整理版)--第2页

{

t=ts+(i-1)*h;

k1=-x[i-1]+2*y[i-1]+6*z[i-1];

m1=-y[i-1]+3*z[i-1]+2*sin(t);

n1=-z[i-1]+sqrt(t)*exp(-t)+cos(t);

k2=-(x[i-1]+k1*(h/2.0))+2*(y[i-1]+m1*(h/2.0))+6*(z[i-1]+

n1*(h/2.0));

m2=-(y[i-1]+m1*(h/2.0))+3*(z[i-1]+n1*(h/2.0))+2*sin(t+

h/2.0);

n2=-(z[i-1]+n1*(h/2.0))+sqrt(t+h/2.0)*exp(-(t+h/2.0))+

cos(t+h/2.0);

k3=-(x[i-1]+k2*(h/2.0))+2*(y[i-1]+m2*(h/2.0))+6*(z[i-1]+

n2*(h/2.0));

m3=-(y[i-1]+m2*(h/2.0))+3*(z[i-1]+n2*(h/2.0))+2*sin(t+

h/2.0);

n3=-(z[i-1]+n2*(h/2.0))+sqrt(t+h/2.0)*exp(-(t+h/2.0))+

cos(t+h/2.0);

k4=-(x[i-1]+k3*(h/2.0))+2*(y[i-1]+m3*(h/2.0))+6*(z[i-1]+

n3*(h/2.0));

m4=-(y[i-1]+m3*(h/2.0))+3*(z[i-1]+n3*(h/2.0))+2*sin(t+

h/2.0);

n4=-(z[i-1]+n3*(h/2.0))+sqrt(t+h/2.0)*exp(-(t+h/2.0))+

cos(t+h