Solution of Differential and Integral Equations with Walsh Functions

Any well-behaved periodic waveform can be expressed as a series of Walsh
functions. If the series is truncated at the end of any group of terms of a given
order, the partial sum will be a stairstep approximation to the waveform. The
height of each step will be the average value of the waveform over the same
interval.
If a zero-memory nonlinear transformation is applied to a Walsh senes,
the output series can be derived by simple algebraic processes. The coefficients
of the input series will change, but there will be no new terms not in the original
groups-
Nonlinear differential and integral equations can be solved as a Walsh series,
since the series for the derivatives can always be integrated by simple table lookup.
The differential equation is solved for the highest derivative first and the result
is then integrated the required number of times to give the solution