Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
Mathematical software for Sturm-Liouville problems
ACM Transactions on Mathematical Software (TOMS)
Path following in scientific computing and its implementation in AUTO
Sourcebook of parallel computing
An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
MATSLISE: A MATLAB package for the numerical solution of Sturm-Liouville and Schrödinger equations
ACM Transactions on Mathematical Software (TOMS)
Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms
Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms
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In molecular reactions at the microscopic level, the appearance of resonances has an important influence on the reactivity. It is important to predict when a bound state transitions into a resonance and how these transitions depend on various system parameters such as internuclear distances. The dynamics of such systems are described by the time-independent Schrodinger equation and the resonances are modeled by poles of the S-matrix. Using numerical continuation methods and bifurcation theory, techniques which find their roots in the study of dynamical systems, we are able to develop efficient and robust methods to study the transitions of bound states into resonances. By applying Keller's Pseudo-Arclength continuation, we can minimize the numerical complexity of our algorithm. As continuation methods generally assume smooth and well-behaving functions and the S-matrix is neither, special care has been taken to ensure accurate results. We have successfully applied our approach in a number of model problems involving the radial Schrodinger equation.