approximate analytic solution of composed linear descriptor operator system using functional analysis approach

This paper focuses on the solvability and approximate analytic solution of composed linear descriptor operator with constant coefficient, using functional (variational) approach. this approach is based on finding a suitable functional form whose critical points are the solution of the proposed problem and the solution of a proposed problem is a critical point of the obtained variational functional defined on suitable reflexive hilbert space since the existence of this approach is based on the symmetry and positivity of the composed linear descriptor operator on hilbert space. the necessary mathematical requirements are derived and proved. a step-by-step computational algorithm is proposed. illustration and computation with the giving exact solution are also proposed.