Computational Experiments with Intuitive Numerical Analysis

Individual First Computational Experiment

Two Point Boundary problem: y'' + pi^2 y = 0; y(0) = 0; y(0.5)=1
Instructor provides a code in Fortran or C solving this problem and computing error at each grid point using known true solution, y(x) = sin pi x. Student must insert calls to the system CPU timer to obtain timing data for cost discuss in written lab report. Student comes to gain measurable understanding of mathematical operation counts of work and measurable accuracy behavior through examining different discretization grid sizes with N = 2, 4, 8, 16, 32, 64 refinements.

Group Second Computational Experiment

Building on experience from exploring and documenting first computational experiment, student groups select a problem of interest to them when they will again investigate cost/work and accuracy in the computed solution.

Group Final Computational Experiment

The group ports their program to the Cray T90 and gathers performance data on the alternate platform so that the final computational experiment written report gives a comprehensive investigative report on performance, highlighting work and accuracy.