An introduction to wavelets
| Hi-index | 31.45 |
An orthonormal basis set composed of Walsh functions is used for deriving global solutions (valid over the entire domain) to nonlinear differential equations that include discontinuities. Function g"n(x) of the set, a scaled Walsh function in sequency order, is comprised of n piecewise constant values (square waves) across the domain x"a=~ can be demonstrated. Fundamental operations (reciprocal, integral, derivative) on Walsh function series representations of functions with discontinuities are defined. Examples are presented for solution of the time dependent Burger@?s equation and for quasi-one-dimensional nozzle flow including a shock.