Mathematical Sciences: Computational Methods for Multiconstrained Nonlinear Variational Problems

拟议的研究集中在一个新的计算 方法开发解决变分问题的大， 可能是无限的一组约束 调查 提出了这种方法的各个方面，重点是 误差分析，离散化技术，推广和 收敛加速 并在此基础上 计算算法预计将开发一个类 平衡和缓慢进化问题， 大量守恒定律的问题。 一大类 在物理和工程中的应用提出了 在这些计算工具的帮助下， 算法应用问题包括理想问题 磁流体动力学（托卡马克设计， 实验数据），流体动力学（设计有效的 具有改进的收敛性和稳定性的计算算法 性质）和天体物理学。 变分方法也提出了发展 求非线性方程周期解的数值方法 波动方程与二阶拟周期解 动力系统

The proposed research is focused on a new computational method developed for solving variational problems with a large, possibly infinite, set of constraints. An investigation of various aspects of this method is proposed, with emphasis on the error analysis, discretization techniques, generalizations and convergence acceleration. On the basis of this method computational algorithms are expected to be developed for a class of equilibrium and slow evolution problems and for evolution problems with a large number of conservation laws. A large class of applications in physics and engineering is proposed for the investigation with the help of these computational algorithms. Applied problems include problems in ideal magnetohydrodynamics (tokamak design, analysis of the experimental data), fluid dynamics (design of efficient computational algorithms with improved convergence and stability properties) and astrophysics. The variational approach is also proposed for developing numerical methods for finding periodic solutions of nonlinear wave equation and quasi-periodic solutions of second order dynamical systems.