The title summarizes my question(s):
- What is a terminal value problem?
- How does it relate to the initial value problem?
- Which methods are used to solve them?
- Can I somehow transform them into an IVP and solve them using e.g. RK4?
- For ordinary differential equations, is the terminal value problem equivalent to solving an initial value problem with negative time? (For example in a spatial domain, the question of an IVP is given a point particle at position X at time T0, find where the particle will be at time T0+T. Logically the question of a TVP would be given a point particle at position X at time T0+T, find where the particle originally was at time T0?)
I have spent time researching the topic online, but they only appear in (mostly Arxiv) research papers which are very hard to follow without a mathematics background. I am writing a C++ library for numeric evaluation of ordinary differential equations, and would like to be as complete as possible, which is the reason for this query.