Mathematical Sciences: Numerical Methods for Nonlinear Variational Problems

这项研究涉及到发展和 通用高效数值算法实现 用于解决广泛的非线性变分问题， 以及非线性特征值问题。 两个互补 原理被用于创建新的计算求解器。 它们是改造目标的方法 功能和使用匹配的数值技术， 解决由此产生的问题。 将使用开发的方法 在许多应用中，包括解决两个和三个 磁流体力学中的维自由边界问题， 为孤立波理论中的问题寻找新的解决方案 流体中的波，并开发新的数值技术， 具有大量守恒律的演化问题。

This research is concerned with the development and implementation of general and efficient numerical algorithms for solving a wide range of nonlinear variational problems as well as nonlinear eigenvalue problems. Two complementary principles are utilized for creating new computational solvers. They are the method of transformation of the objective functional and the use of matching numerical techniques for solving the resulting problem. Methods developed will be used in a number of applications which include solving two and three dimensional free boundary problems in magnetohydrodynamics, finding new solutions for problems in the theory of solitary waves in fluids, and developing new numerical techniques for evolution problems with a large number of conservation laws.