Math Is Fun Forum

Ancalagon

Member

Registered: 2011-01-10

Posts: 3

Problem with Numerical Integration

I'm currently having difficulties trying to numerically integrate the following

where A and B are constants. I need to determine this integral for values all values x such that

. I have solved this integral analytically for the special case of

successfully. I am now interested in examining the integral for cases when alpha does not equal one. However, I am currently unable to numerically integrate this function.  I currently get correct solutions for x >0 and complex solutions for x <1 when solved numerically for alpha = 1 while the analytical solution correctly gives only real answers. I think I am incorrectly numerically integrating this function. Can anyone show me how they would integrate this? My background is in Physics and I am only aware of some very basic numerical integration techniques.

Thanks for any help you can give me with this.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Problem with Numerical Integration

Hi Ancalagon;

Offhand I would say, who would not have trouble. For Forman S. Acton that might be a piece of cake but for his students that are much less talented some questions have to be asked.

The top bracket, are we dealing with an integer part or just a bracket? Please provide your constants ( as many as you can ) or at least bounds on them. You might be able to do that by a knowledge of the process that created this integral.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Ancalagon

Member

Registered: 2011-01-10

Posts: 3

Re: Problem with Numerical Integration

Both A and B are constants which are between 0 and 1. The top bracket is just a bracket.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Problem with Numerical Integration

My background is in Physics and I am only aware of some very basic numerical integration techniques.

What numerical techniques have you used? The value of r?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Ancalagon

Member

Registered: 2011-01-10

Posts: 3

Re: Problem with Numerical Integration

Success! By using Gauss–Kronrod quadrature I was able to successfully numerically integrate this function. Thanks for you help!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Problem with Numerical Integration

Whoa! Whoa! May I see what you did?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.