NUMERICS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS OF PARABOLIC TYPE

点击翻译按钮获取中文摘要

Stochastic partial differential equations (SPDEs) are an essential tool in the description of complex systems affected by external or internal fluctuations arising in physics, chemistry, biology, finance. Effective numerical methods play crucial role in studying models described by SPDEs. Numerics for SPDEs is a relatively new area of stochastic numerical analysis and its further development is essential for both practice and theory. We well know how it is important to have a large arsenal of methods for deterministic equations. This is even more important in the case of SPDEs due to their higher complexity. The proposed research will develop the new approach to numerics for SPDEs and give new methods together with their rigorous analysis using novel ideas of layer methods. The proposed methods will be tested on model problems.