Hi, I need to calculate some discrete variational problems, but it's a hard work just by hand.
Is there any toolboxes about the discrete variational computation? Or how to design a program to do that?
In particular, I need to realize the functions:
1. the linearized operator and the adjoint operator of some expressions.
the linearized operator of u(n,m+1)u(n+1,m) is u(n+1,m)Tm+u(n,m+1)Tn
the adjoint operator is u(n+1,m-1)T^(-1)m+u(n-1,m+1)T^(-1)n,
(The latter is just the discrete Euler operator.)
Tm, Tn is the shift operator, T^(-1) is the inverse operator of T.
2. discrete Euler-Lagrange equation.
I am not familar with the maple, please help!