Numerical integration
- To: mathgroup at smc.vnet.net
- Subject: [mg73781] Numerical integration
- From: "dimitris" <dimmechan at yahoo.com>
- Date: Wed, 28 Feb 2007 04:34:31 -0500 (EST)
In another post I talk about the integral Integrate[Cos[a x] CosIntegral[b x], {x, 0, Infinity}] I have problems to numerical integrate this function for say {a,b}={3,2}. In[20]:= Integrate[Cos[3*x]*CosIntegral[2*x], {x, 0, Infinity}] N@% Out[20]= -(Pi/6) Out[21]= -0.5235987755982988 No matter how I set Options I couldn't get satisfactory results by NIntegrate. Any ideas will be greatly appreciate! Here is its plot In[59]:= Plot[Cos[3*x]*CosIntegral[2*x], {x, 0, 10}, Ticks -> {Range[0, 10*Pi, Pi/6], Automatic}] As we see the zeros if the function are situated at Pi/6 + n*(Pi/3), n=0,1,2,3... In[61]:= (Cos[3*#1]*CosIntegral[2*#1] & ) /@ Table[Pi/6 + n*(Pi/3), {n, 0, 100}] Out[61]= {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,\ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,\ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} I tried to take use of this fact doing something like In[67]:= lst = Table[Pi/6 + n*(Pi/3), {n, 0, 1000}] /. {a_, b__, c_} -> {x, 0, a, b, c}; In[70]:= NIntegrate[Cos[3*x]*CosIntegral[2*x], Evaluate[Sequence[lst]], WorkingPrecision -> 40] NIntegrate::ncvb :.... -0.52359885758572151495786704 Very good result but I look for any other methods/settings! Dimitris