Solve recurrence relations using Mathematica

[winterorchids]

Hello,

I was hoping someone could help point me in the right direction. I am trying to figure out how to solve recurrence relations using Mathematica (6). I have tried to search the web for information on how to use the recurrence relation solving package but I must be doing something wrong. I did a Google search for recurrence relations Mathematica and the only thing I found that seemed accessible to me was a link to The Mathematica Book by Wolfram which told me to enter the command below... which gave me an error. It said with some versions you don't need to load it so I tried the equation given and it didn't return a proper result.

<< DiscreteMath' RSolve'

Get::noopen: Cannot open DiscreteMath. RSolve::argmu: RSolve called with 1 argument; 3 or more arguments are expected.

An example problem that I would like to be able to solve is:
T(n) = T(n-1) + 2T(n-2)

Any links or tutorials would be helpful! Otherwise, if Mathematica isn't the way I should be going about this I am all for other suggestions!

Thank you for your time and patience!
----

*It should be noted that I am fairly bad at Math and unskilled at Mathematica. I am definitely a "newbie" so :) I apologize if the answer is right in front of my face.* I am attempting to ask "intelligent" questions after I've tried for quite a while to figure it out on my own/do my own research.

 

[Crosson]

What version of Mathematica are you using? In version 6.0 you can type:

RSolve[T[n] == T[n - 1] + 2 T[n - 2], T[n], n]

and the output is:

{{T[n] -> (-1)^n C[1] + 2^n C[2]}}

You could eliminate the undetermined constants by giving initial conditions:

RSolve[{T[n] == T[n - 1] + 2 T[n - 2].T[0]==0,T[1]==1}, T[n], n]

for which the output is:

{{T[n] -> 1/3 (-(-1)^n + 2^n)}}

 

[oswaler]

Hello,

Thank you for reaching out for help with solving recurrence relations using Mathematica. I am a scientist and have experience using Mathematica for various mathematical computations. I understand your frustration with trying to figure out how to use the recurrence relation solving package in Mathematica. It can be a bit tricky to figure out at first, but with some practice and guidance, you will be able to solve recurrence relations easily using Mathematica.

First, let's address the error you encountered when trying to load the DiscreteMath' RSolve' package. This package is used for solving discrete mathematical problems, including recurrence relations. In order to use this package, you need to first load it into Mathematica using the command:

<<DiscreteMath'RSolve'

If you receive an error, it could be due to a few reasons. First, make sure you are using the correct version of Mathematica. The DiscreteMath' RSolve' package may not be available in older versions. Additionally, make sure you are using the correct syntax for the command. It should be typed exactly as shown above, with no spaces between the words and the apostrophes.

Now, for solving the example recurrence relation T(n) = T(n-1) + 2T(n-2), we can use the RSolve function in Mathematica. The syntax for this function is:

RSolve[{T(n) == T(n-1) + 2T(n-2)}, T(n), n]

This will return a general solution for T(n). If you want to find a specific value for T(n), you can substitute a number for n in the general solution. For example, to find T(5), you can use:

RSolve[{T(n) == T(n-1) + 2T(n-2)}, T(n), n] /. n -> 5

I hope this helps you get started with solving recurrence relations using Mathematica. There are also many tutorials and resources available online that can help you learn more about using Mathematica for mathematical computations. Don't hesitate to reach out for help if you encounter any further issues. Good luck!