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.
