Numerical Analysis

A generalized conjugate direction method and its application on a singular perturbation problem.- Some implementation schemes for implicit Runge-Kutta methods.- Best approximation in tensor product spaces.- Monotonicity and free boundary value problems.- Computing eigenvectors (and eigenvalues) of large, symmetric matrices using Lanczos tridiagonalization.- Horizontal line analysis of the multidimensional porous medium equation: Existence, rate of convergence and maximum principles.- Numerical methods for phase-plane problems in ordinary differential equations.- On the use of exact penalty functions to determine step length in optimization algorithms.- Petrov-Galerkin methods for non-self-adjoint problems.- Collocation and perturbed collocation methods.- Modular analysis of numerical software.- The numerical solution of turbulent flow problems in general geometry.- The rate of convergence of a multiple grid method.