Hello again! I have been working on proposal since aproximately 15 of April, investigating boost odeint, some theory of numeric methods of solving ODE and implementing a draft of the design of implicit routines. I discussed some issues privately with mentors of odeint project Mario Mulansky and Karsten Ahnert and have taken into account all the points. Here is the 1st version of the proposal for Boost.odeint implicit routines. Note: The main idea i kept in mind was to describe steps how i will do the project as clear and detailed as possible. I tried to show my acquired experince of odeint structure and concepts, my understanding of the issue and concrete ways of tackling it. Note: The proposal entirely lacks introduction, list of literature and sources! i will settle it as soon as possible. Here is the link to the proposal: https://docs.google.com/file/d/0B-2QwVSmhDBIYTB0eVZxdHhsNUE/edit?usp=sharing -- Thanks, Artem Serov