Walsh spectral analysis for ordinary differential equations. I. Initial value problems

Walsh spectral analysis is applied to ordinary differential equations. It is shown that the method is directly equivalent to trapezoidal integration for first-order differential equations. This is a consequence of the finite-dimensional integration operator being of lower triangular Toeplitz form. The method is applied to equations with discontinuous forcing functions, and the numerical results are shown to be superior to those given by either Fourier spectral analysis or Runge-Kutta methods