Euler-Lagrange as a Sparse matrix

  1. Hello,
    I want to represent Euler-Lagrange equations in a (sparse) matrix form, such that; Az=b.
    (in order to improve performance when solving).
    I know A should be diagonal block, very large, and sparse.
    my equations are:

    1. -ψ'(Ix*Iz) + [itex]\gamma[/itex]ψ'(Ixx*Ixz + Ixz + Ixy*Iyy) - βη(ψ'(u-u1).
    2. -ψ'(Iy*Iz) + [itex]\gamma[/itex]ψ'(Iyy*Iyz + Ixy*Ixz) - βη(ψ'(v-v1).

    η - means some kind of neighboring of u.

    I know it should looks something like:
    Az=b:
    where
    z = [u1 v1 u2 v2 ....un vn]τ (column vector).
    b = - [ψ'xz + βηU IxIz + βηV ... ] (Alternately) --> I'm not so sure here..
    and A is very large, and saprse, of size 2*(n*n) - where n is the number of values I have.

    Are z and b correct ? How should A be constructed ?
    Thanks
    Matia
     
  2. jcsd
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