The bellman pseudospectral method is a way of solving a complicated mathematical problem called a dynamic optimization problem. It works by taking the complicated problem and breaking it down into a bunch of pieces, kind of like a puzzle. Each piece can be solved separately, and then all of the pieces are put back together to solve the original problem. It's like when you clean your room and you work in sections, putting all the toys in one spot, all the books in another and all the clothes in another. Once it's all done, you have a clean room!