Converting a cis-alkene to trans-alkene I was thinking about simple method to convert a cis-alkene alkene like cis-2-butene to trans-2-butene.
I came up with this method (the method can also be used to convert trans alkene to cis alkene):

First use a peracid like m-CPBA to convert the cis alkene to an epoxide:


Then I used the Wittig reagent $\ce{PPh_3}$ to get a betaine. For the $\ce{- O-}$ to be able to attack $\ce{PPh3}$, they should be on same side. So rotation about $\ce{C-C}$ bond:




Finally, the leaving of $\ce{POPh3}$:


I would like to know if my method is correct and if there are any other methods to bring about the conversion.
Your method looks fine. There is another simple method (with three steps though).

Convert the the cis alkene to a dibromo derivative using bromine;
Use two equivalents of $\ce{NaNH2}$ to get an alkyne (elimination);
Selective reduction to trans alkene by using sodium in liquid ammonia.
However this requires that Hydrogen be present as a substituent on the double bond, on both carbons.