# Need help updating an old Mathematica worksheet

I found a notebook that symbolically applies the multiple time scales method to any differential equations. I don't like just using other people's code so I am going through the author's work line by line. I am new to Mathematica so I am looking up each function and reading about the syntax as I go through the code. Unfortunately I am running into issues because it appears the Mathematica language has changed since the creation of the notebook.

I think I was able to fix the first error I received by removing the <<Algebra ReIm; line since it seems ReIm is an outdated package. The second error I am receiving is

Function::flpar: "Parameter specification {T[0],T[1]} in
Function[{T[0],T[1]},Cos[ω\ T[0]]\ C[1][T[1]]+Sin[ω\ T[0]]\
C[2][T[1]]] should be a symbol or a list of symbols."

Which I get from line

zerosol = DSolve[zeroordereqn == 0,
x[0], {T[0], T[1]}] /. {C[_][#2]*Cos[omega_.*#1] + C[_][#2]*Sin[omega_.*#1] ->
A[#2]*Exp[I*omega*#1] + Conjugate[A[#2]]*Exp[-I*omega*#1]}


I am not sure how to fix this error, I believe it has to do with T[ 0 ] and T[ 1 ] not being initialize properly. I would appreciate any help with the issue.

I am sorry if this is a simple question, but I am pretty new to Mathematica and not sure where to look to find the solution.

Casey

The error itself may be isolated to this operation:

zeroordereqn = ω^2 x[0][T[0],T[1]]+(x[0]^(2,0))[T[0],T[1]];

DSolve[zeroordereqn == 0, x[0], {T[0], T[1]}]


DSolve gives a result in terms of a Function using the parameters T[0] and T[1] but this is not valid. Perhaps at some time DSolve gave different output but I cannot test that. However if one replaces T[0] and T[1] with t0 and t1 the error is avoided:

DSolve[zeroordereqn == 0 /. {T[0] -> t0, T[1] -> t1}, x[0], {t0, t1}]

{{x[0] -> Function[{t0,t1},Cos[t0 ω] C[1][t1]+Sin[t0 ω] C[2][t1]]}}


The fancy replacement at follows the DSolve however has no effect which leads me to believe that the output format is no longer compatible with this Notebook.

• @Casey: I agree, but would start from the beginning, which is fixing InPowers using Symbol instead of indexed variables for T and x and working down. Therefore, it would be most useful to keep the unmodified workbook open and start out new by copy-pasting and using up-to-date Mathematica methods as you go. Commented Feb 26, 2015 at 2:31
• @Jinxed Do you understand the transformation that was intended by the replacement following DSolve? Commented Feb 26, 2015 at 2:54
• I am pretty sure, that it is converting the pure function generated by the old Mathematica from trigonometrical to exponential form. Commented Feb 26, 2015 at 10:48
• I think I will have a go on this old notebook this afternoon and try to bring it up-to-date from top to bottom. Let's see, if I manage to and how long it might take. Commented Feb 26, 2015 at 10:56

I managed to update the workbook for Mathematica-10-compatibility, but stopped just before the section Duffing Equation.

I also did not copy the original explanatory texts (yet), since this will need some refurbishing also.

Here is what I managed so far (just copy, paste and execute):

NotebookPut@Uncompress@"1:eJztPQ10HMV5si1kGwcMOAHS8OjZBNtyT7LuJGNLxQJbP0
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