Numerical implementation of coherence for the example of the 'Swiss Cross'.

We consider the two-dimensional Helmholtz equation Δ u+λ u=0 in D with the boundary conditions u=0 on ∂ D. D is the 'Swiss Cross' - a region consisting of five unit squares. A method based on the concept of 'Coherence' is utilized to determine an approximation for the first eigenvalue λ= λ more accurate than calculated by classical difference methods. The numerical result is used to illustrate isoperimetric upper and lower bounds for λ, and to test some conjectures on its relations with torsional rigidity. [ABSTRACT FROM AUTHOR]