On Direct Algebraic Solutions of Linear Differential Equations using Walsh Transforms

Walsh Functions and their Applications: A Review

“…New ideas were proposed by Rao [70][71][72][73][74][75][76] and Chen [77][78][79][80][81][82]. Other notable workers were Le Van et al [83], Tzafestas [84], Chen [85][86][87][88], Mahapatra [89], Paraskevopoulos [90], Moulden [91], Deb and Datta [92][93][94], Lewis [95], Marszalek [96], Dai and Sinha [97], Deb et a/ [98-1 00] and others.…”

“…This was done independently by Rao [70], Chen [77] and Le Van eta/ [83]. LeVan sensed that since the integral operator matrix had an inverse, the inverse must be the differential operator in the Walsh domain.…”

On Analytical Techniques of Power Electronic Circuit Analysis

“…From this we see that frequency can be regarded as a special measure of sequency applicable to sinusoidal waveforms only. The first positive step in Walsh domain analysis was the formulation of the operational matrix for integration G and differentiation D. These are square matrices with real elements and as the names suggest, D is the imerse of G. These operational matrices were developed independently by Rao [47], Chen [48,49] and LeVan et a/ [50]. Chen presented Walsh domain analysis with the operational matrices for integration as well as differentiation to solve various problems relating to linear as well as nonlinear systems.…”