NONSEPARABLE SOLUTIONS OF THE HELMHOLTZ WAVE EQUATION EXAMINED FOR APPLICATIONS
Final technical rept.
VITRO LABS SILVER SPRING MD
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A conventional solution of the Helmholtz or time-reduced wave equation is a simple product of functions that contain one coordinate variable in each. An unbounded set of solutions that are not separable into simple products of single-variable functions has been partially examined for applicability to vibrational problems. Applications to scalar usage have been found, and illustrations including shapes and frequencies for membranes and an acoustic cavity are reported. Efforts to make application to vector usage are described, as are numerous mathematical properties that have been discovered in the course of the work. It is concluded that vibration on or within some new shapes can now be calculated exactly with functions formed of the nonseparable solutions added to separable solutions. It is also concluded that simplifications in the mathematics and additional applications await the effort.
- Numerical Mathematics