A Python implementation of modern Adaptive Multistep methods in the object oriented simulation tool Assimulo

Linear multi-step methods have been around for more than a century now. But they were with a fixed step-size, where a lot of hand calculations had to be made to find the coefficients of each method separately. It is only recently that variable step-size methodology was introduced and built into the solver. In this thesis, we are exploring this new methodology and at the same time, implementing one of it's methods in Object-Oriented Simulation Tools called Assimulo, so that the method is industrially available for solving real life problems. We will first give an introduction of the linear multi-step methods. Then we will dive into the methodology itself. After this we will give an introduction of the simulation tool: Assimulo and how it works. Then we will come to the main part of the thesis i.e implementing these ideas in Assimulo. We will describe each phase of the implementation process separately, along with an overview of the obstacles faced and how they were tackled. The last section, before conclusion, will then be the experiments, where we have tested the new method in Assimulo by comparing our solver's performance with a variable step-size and variable order solver called CVODE. Last, we have a conclusion where we have summarized our results. We have found that although more work needs to be done in Assimulo, this new solver gives us results close to the CVODE, which is a C++ based solver/package. (Less)