Robust and reliable software for the investigation of approximate solutions of systems of ordinary differential equations

点击翻译按钮获取中文摘要

In the proposed research we plan to analyze and improve the reliability, robustness and usefulness of numerical software for approximating the solution of differential equations. We will analyze and develop effective tools for the visualization and verification of approximate solutions and for investigating other issues of particular interest to practitioners developing mathematical models in a variety of different application areas. These areas include medicine, ecology, biology and finance. Our contribution and will not be to the development of new or better mathematical models, but rather we will provide a mechanism that will help practitioners understand and tune the parameters of their model to better fit the observed behaviour of the system they are modeling.