December 12, 2018

Numerical and Computational Challenges in Science and Engineering Program

Ian Gladwell
Department of Mathematics, Southern Methodist University


Friday, October 26, 2001, 2:00 pm, room 230

Variable step methods for model Hamiltonian Systems

We consider the implementation of a variety of variable step size methods for partitioned Hamiltonian systems. Some of these methods are Hamiltonian preserving. To test the implementations we use some commonly occurring model partitioned Hamiltonian systems. We study the impact of the step size adaptivity strategy on the cost and quality of solutions of problems of a range of difficulties. Particularly, we are concerned with the effects of iteration and accumulated roundoff error, and of limited precision.

This is joint work with Valeria Antohe.

Friday, September 28, 2001, 10:00 am, room 230

Almost block diagonal (ABD) linear systems arise in the discretization of boundary value problems in differential equations when there are separated boundary conditions, e.g. for problems with Dirichlet
boundary conditions. When the boundary conditions are non-separated, e.g. for periodic boundary conditions, the corresponding system is bordered almost block diagonal (BABD).

We show by example why the standard Gaussian elimination algorithm when used to solve a BABD system might fail, and we consider alternative algorithms which work with the BABD structure. We discuss the performance of the MATLAB dense and sparse linear system library functions on this BABD problem.

Finally, we show how to convert a BABD system to a larger ABD system and discuss the use of standard and specially designed ABD algorithms for this transformed system.

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