搜搜做题作业网菜鸟!急问!求助一个Mathematica做积分的问题!
来源：学生作业帮 编辑：搜搜做题作业网作业帮 分类：数学作业 时间：2024/04/28 05:15:23
菜鸟!急问!求助一个Mathematica做积分的问题!
程序如下：
In[1]:=6*1.1^3*NIntegrate[
Exp[-0.03*(s + x + v) - 0.002*(x^2 + s^2 + v^2)/2 +
0.001^2/6*(s^3 - 3*s*x^2 + 6*x^3 - 12*x*v^2 + 17*v^3)],{v,0,
1000},{x,v,1000},{s,x,1000}] -
6*3*1.1^2*
NIntegrate[
Exp[-0.03*(s + x + v) - 0.002*(x^2 + s^2 + v^2)/2 +
0.001^2/6*(s^3 - 3*s*x^2 + 6*x^3 - 12*x*v^2 + 17*v^3)],{v,0,
1000},{x,v,1000},{s,x,1000}] +
2*3*1.1*NIntegrate[
Exp[-0.03*(s + 2*v) - 0.002*(s^2 + 2*v^2)/2 +
0.001^2/6*(17*s^3 + 12*v*s^2 + 4*v^3)],{v,0,1000},{s,0,
v}] + 2*3*1.1*
NIntegrate[
Exp[-0.03*(s + 2*v) - 0.002*(s^2 + 2*v^2)/2 +
0.001^2/6*(s^3 - 3*s*v^2 + 11*v^3)],{v,0,1000},{s,v,
1000}] +
6*3*1.1*NIntegrate[
Exp[-0.03*(s + u + v) - 0.002*(u^2 + s^2 + v^2)/2 +
0.001^2/6*(s^3 - 3*s*u^2 + 6*u^3 - 12*u*v^2 + 17*v^3)],{v,0,
1000},{u,v,1000},{s,u,1000}] - 6682.90
出来如下的结果：NIntegrate::slwcon:Numerical integration converging too slowly; suspect one of the following:singularity,value of the integration is 0,highly oscillatory integrand,or WorkingPrecision too small.>>
NIntegrate::slwcon:Numerical integration converging too slowly; suspect one of the following:singularity,value of the integration is 0,highly oscillatory integrand,or WorkingPrecision too small.>>
NIntegrate::slwcon:Numerical integration converging too slowly; suspect one of the following:singularity,value of the integration is 0,highly oscillatory integrand,or WorkingPrecision too small.>>
General::stop:Further output of NIntegrate::slwcon will be suppressed during this calculation.>>
Out[1]=2.704725569675203*10^1045
Ps.上面是积分限取1000的结果,积分限取800的时候等于1.321678837009696*10^357
可是积分的指数函数应该是收敛的.怎么会越来越大了呢?
程序如下：
In[1]:=6*1.1^3*NIntegrate[
Exp[-0.03*(s + x + v) - 0.002*(x^2 + s^2 + v^2)/2 +
0.001^2/6*(s^3 - 3*s*x^2 + 6*x^3 - 12*x*v^2 + 17*v^3)],{v,0,
1000},{x,v,1000},{s,x,1000}] -
6*3*1.1^2*
NIntegrate[
Exp[-0.03*(s + x + v) - 0.002*(x^2 + s^2 + v^2)/2 +
0.001^2/6*(s^3 - 3*s*x^2 + 6*x^3 - 12*x*v^2 + 17*v^3)],{v,0,
1000},{x,v,1000},{s,x,1000}] +
2*3*1.1*NIntegrate[
Exp[-0.03*(s + 2*v) - 0.002*(s^2 + 2*v^2)/2 +
0.001^2/6*(17*s^3 + 12*v*s^2 + 4*v^3)],{v,0,1000},{s,0,
v}] + 2*3*1.1*
NIntegrate[
Exp[-0.03*(s + 2*v) - 0.002*(s^2 + 2*v^2)/2 +
0.001^2/6*(s^3 - 3*s*v^2 + 11*v^3)],{v,0,1000},{s,v,
1000}] +
6*3*1.1*NIntegrate[
Exp[-0.03*(s + u + v) - 0.002*(u^2 + s^2 + v^2)/2 +
0.001^2/6*(s^3 - 3*s*u^2 + 6*u^3 - 12*u*v^2 + 17*v^3)],{v,0,
1000},{u,v,1000},{s,u,1000}] - 6682.90
出来如下的结果：NIntegrate::slwcon:Numerical integration converging too slowly; suspect one of the following:singularity,value of the integration is 0,highly oscillatory integrand,or WorkingPrecision too small.>>
NIntegrate::slwcon:Numerical integration converging too slowly; suspect one of the following:singularity,value of the integration is 0,highly oscillatory integrand,or WorkingPrecision too small.>>
NIntegrate::slwcon:Numerical integration converging too slowly; suspect one of the following:singularity,value of the integration is 0,highly oscillatory integrand,or WorkingPrecision too small.>>
General::stop:Further output of NIntegrate::slwcon will be suppressed during this calculation.>>
Out[1]=2.704725569675203*10^1045
Ps.上面是积分限取1000的结果,积分限取800的时候等于1.321678837009696*10^357
可是积分的指数函数应该是收敛的.怎么会越来越大了呢?
有奇点或者被积函数小于零,所以发散了哦.积分上限取800时出来的结果也是错的.你可以先把被积函数画出来,看是不是有奇点,然后可以分段积分,跳过奇点.