# NDSolve differences between mathematica 8 and 9

• Mathematica
• EnSlavingBlair
In summary, the user is having trouble with a particular expression on Mathematica 9, but it worked on Mathematica 8. The expression involves NDSolve and has an imaginary number. Mathematica 8 gave a result of an interpolating function, while Mathematica 9 gave an error message. The user is seeking help to understand the issue and cannot access Mathematica 8 regularly. The expert advises to use capital "I" for the imaginary number instead of escaping it.
EnSlavingBlair
Hello,

I am using mathematica 9 and having some problems with a particular expression, but when I tried it on mathematica 8 it worked perfectly. My expression is:

NDSolve[{D[T[n,z], n]+i 2 D[T[n,z], {z,2}]+z^2 T[n,z]==0, T[0,z]==1, Derivative[0,1][T][n,5]==0, Derivative[0,1][T][n,0]==0}, T, {n,0,5}, {z,0,5}]

where i is the imaginary number, and on both I had a new window to work on, with nothing having been done previously on it.

Mathematica 8 gave me this:
{{T-> InterpolatingFunction[{{0.,5.},{0.,5.}},<>]}}

and mathematica 9 gave me this:
NDSolve::ndnum : Encountered non-numerical value for a derivative at n==0.`.>>

Does anyone know what is going on here? I cannot use mathematica 8, as I do not have continual access to that machine.

The imaginary number in my code was entered as :esc: I :esc: not as the lower case i.

Don't escape "I" for imaginary. Just use capital "I". :I: is capital Iota.

## 1. What are the major differences between NDSolve in Mathematica 8 and 9?

The major differences between NDSolve in Mathematica 8 and 9 include improved performance and support for more types of differential equations in version 9. Additionally, version 9 introduced new features such as automatic error control and adaptive precision, as well as improved syntax for specifying initial conditions.

## 2. Can NDSolve in Mathematica 9 solve the same types of differential equations as version 8?

Yes, NDSolve in Mathematica 9 can solve all of the same types of differential equations as version 8, plus additional types such as delay differential equations and differential-algebraic equations.

## 3. Are there any known compatibility issues when upgrading from Mathematica 8 to 9 for NDSolve?

While most code written for NDSolve in Mathematica 8 should work in version 9 without any changes, there have been some reported compatibility issues with specific functionalities. It is recommended to test your code thoroughly after upgrading to ensure everything is working as expected.

## 4. Does NDSolve in Mathematica 9 have any new features or improvements?

Yes, NDSolve in Mathematica 9 introduced several new features and improvements, including faster and more efficient algorithms, improved accuracy and stability, and new options for specifying boundary conditions and solving complex problems.

## 5. Can I still use NDSolve in Mathematica 8 even after upgrading to version 9?

Yes, you can still use NDSolve in Mathematica 8 after upgrading to version 9. However, it is recommended to update your code to take advantage of the new features and improvements in version 9 for optimal performance and accuracy.

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