#2434 Romberg Integral yields zero value

closed
nobody
5
2012-09-21
2012-07-01
MukundNaik
No

build_info("5.27.0","2012-05-08 11:27:57","i686-pc-mingw32","GNU Common Lisp (GCL)","GCL 2.6.8")

m1(x):=(1-cos(%pi*x))*(1-cos(%pi*x*2/3))*(1-cos(%pi*x*2/5))*(1-cos(%pi*x*2/7))/16;

wxplot2d([m1(x)], [x,32,36], [y,0,0.6],
[gnuplot_preamble, "set grid;"])$

romberg(m1(x), x, 32, 36); yields Zero. The plot above shows that it is not zero everywhere in the region 32-36. In fact,
romberg(m1(x), x, 32, 33) = 0.051305498551289
romberg(m1(x), x, 33, 34)=0.016230140453864
romberg(m1(x), x, 34, 35)=0.0014305334087985
romberg(m1(x), x, 35, 36)=2.3489482722215246*10^-4.

Discussion

  • Raymond Toy

    Raymond Toy - 2012-08-15

    1. Update summary to reflect this is a romberg issue, not symbolic integration.
    2. Change category to floating-point
    3. Changed visibility to non-private.

    Try changing some of the variables that control romberg integration. Changing rombergmin to 1 gives romberg(m1(x),x,32,36) -> 0.0692, which is very close to the value of the symbolic integral.

     
  • Raymond Toy

    Raymond Toy - 2012-08-15
    • summary: Definite Integral yields zero value --> Romberg Integral yields zero value
    • labels: 840495 --> Lisp Core - Floating point
    • status: open --> pending
     
  • Raymond Toy

    Raymond Toy - 2012-09-21
    • status: pending --> closed
     

Log in to post a comment.